(313b) Ultrafiltration Optimization Via Experimental Design
Separation and recovery of proteins are important processes in biotechnology. Various techniques are used for protein separation including chromatography, electrophoresis, and membrane ultrafiltration among others. Limitations of chromatography or electrophoresis include in some cases dilution of product, difficulty with high titer (i.e. highly viscous) solutions, scale up and the cost of the instrumentation. At the same time, membrane ultrafiltration has received a significant amount of attention because of its scalability and economics.
Membrane-based unit operations have been traditionally viewed as size-based separation processes where the size of the solutes differs by at least an order of magnitude . However, factors other than molecular sieving can also affect the performance of ultrafiltration. For example, concentration polarization  and electrostatic interactions between proteins and proteins and membranes  have been investigated for the separation of proteins of similar size. The effect of pH on fractionation of proteins of similar size has been investigated by van Eijndhoven et al. [4, 5].
Optimization of factors affecting UF has been studied due to the strong dependence of UF performance on these factors [6,7,8]. The main challenge of fundamental approaches for this task is that they use models involving particle-particle interactions and resolving the resulting complex expressions requires significant computational effort. An alternative approach is to use experimentally generated data to predict membrane UF performance. However, the number of experiments to perform such optimizations can be large, resulting in significant time and financial commitments. This situation presents a clear need for optimal experimental design which can be used to either reduce the number of experiments or to maximize the information content from a pre-determined number of experiments.
In this work we present an empirical approach for optimizing operating parameters of UF. A polynomial model is fitted to available experimental data and optimal operating conditions are determined by optimizing the prediction of the model. The models include the factors that can be varied as inputs and they predict certain performance measures of interest. Special attention is paid to the order of the polynomial using cross-validation as the order is affected by the amount of data but also by trends in the data.
There are several performance measures that are commonly used, depending on how the separation process is used. The presented approach can compute operating conditions for different individual performance measures or some combination of them. The resulting expression for the performance measures can be numerically optimized to determine operating conditions that maximize the performance measures. This type of approach is in stark contrast to commonly used linear approaches where one factor is varied at a time. Here, using our nonlinear approach, we are able to account for nonlinearities and interactions among the factors.
The polynomial regression method is illustrated with two case studies. One study involves available experimental data from our lab  and another study uses a data-derived model from the literature . The first case study illustrates that the optimal operating conditions can be significantly different from the ones found by individually varying the parameters, i.e. using a linear approach. The second case study illustrates that the model order should be chosen as low as possible, while still being able to fit the data well, if the main goal is to optimize a performance measure.
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