Ind. Eng. Chem. Res. 1994,33, 2668-2687
2668
An Expert Network for Predictive Modeling and Optimal Design of
Extractive Bioseparations in Aqueous Two-Phase Systems D. Richard Baughman and Y. A. Liu' Department of Chemical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0211
This paper presents a flexible approach to the predictive modeling and optimal design of extractive bioseparations in aqueous two-phase systems (ATPs) using polyethylene glycol (PEG) and dextran. We combine the qualitative reasoning skills of a n extractive-separation expert system with the quantitative modeling capabilities of a protein-partitioning neural network. The resulting hybrid system, called an expert network, provides an accurate and efficient tool for quantitative predictions of phase diagrams and partition coefficients (i.e,, separation factors). We demonstrate the use of the neural-network and response-surface modeling a s a bioseparation optimizer to facilitate experimental design and process development of extractive separation flowsheets for multicomponent protein mixtures in ATPs. We describe the advantages and limitations of our protein-partitioning network when compared to available theoretical models for protein partitioning. In particular, our protein-partitioning network is compartmentalized into physically identifiable subsystems. Therefore, research advances in specific areas can be easily incorporated without major development or reconstruction. 1. Introduction
This paper describes a flexible approach to the predictive modeling and optimal design of extractive bioseparations in aqueous two-phase systems (ATPs). Our primary bioseparation of interest is protein purification, which is a major sector of the biochemical industry that will benefit from a large increase in capacity to develop to its full potential. Liquid-liquid extraction, using ATPs, shows promise for cost-effective, large-scale protein purification that can achieve high selectivity and purity requirements (Michaels, 1992). One of the most well-known applications involves the protein partitioning in an ATPs with two polymers, polyethylene glycol (PEG) and dextran, as illustrated in Figure 1 (Clark, 1989). Here, we represent the partition behavior of a protein by a partition coefficient, denoted by Kp, which is defined as the ratio of the protein concentration in the top, PEG-rich phase to that in the bottom, dextran-rich phase. An ATPs that holds great potential is affinity partitioning, which is based on a biospecific ligand either present in or bound to the PEG phase to increase selectivity (Kamihira et al., 1992). Another ATPs or significance uses electrophoresis to obtain improved resolutions (Clark, 1989). Dr. Alan S. Michaels, a well-known expert in biotechnology, has suggested that an important research need in protein partitioning in ATPs is the development of a predictive rationale for selecting the appropriate polymer systems useful for specific protein-recovery requirements (Michaels, 1992). In a recent review, King (1992) states that continued research in the areas of predictive design correlations and development of novel applications and polymers will accelerate the adoption of ATPs in the biotechnology industry. Our research represents a novel application of artificial intelligence to bioseparation process synthesis. We propose to combine the qualitative modeling skills of an expert system with the quantitative modeling capabilities of a neural network, t o develop a n expert network for bioseparation process synthesis, particularly protein partitioning in ATPs.
* To whom correspondence should be addressed. 0888-5885l94l2633-2668$04.50lO
PEG-Rioh Phase 5.7 %PEG 1 .O % Dextran 93.3 %Water
Dextran-Rioh Phase
I
I
W
1.9 Yo PEG 9.5% Dcxtran 88.6% Water
Figure 1. An aqueous two-phase system (ATPs) involving polyethylene glycol (PEG)and dextran (Clark, 1989).
Specifically, our objective is to develop an expert network for protein partitioning in ATPs that is capable of (1)predicting the partition coefficients (i.e., separation factors) over wide ranges of protein properties, ion properties, polymer-solution properties and (2) identifying the optimal separation conditions for multicomponent protein solutions to assist in experimental design and process development.
2. Previous Work There is a large body of published literature on protein partitioning in ATPs. See, for example, (a) review monographs (Albertsson, 1986; Walter et al., 1985),(b) review papers (Baskir and Hatton, 1989; King 19921, (c) conference proceedings (Fisher and Sutherland, 1989),(d)fundamental studies (Baskir et al., 1987; Cabezas et al., 1992; Connemann et al., 1992; Diamond, 1990; Forciniti, 1991; Haynes et al., 1993; King et al., 1988; Mahaderan and Hall, 1990, 1992; Vlachy et al., 19931, (e) tutorial articles (Clark, 19891, (0 recent doctoral dissertations (Diamond, 1990; Forciniti, 1991; Haynes, 1992);(g) affinity partitioning (Ichikawa et al., 1992; Johansson and Tjerneld, 1989; Kamihira et al., 1992; Tjerneld et al., 19871, (h) large-scale applications
0 1994 American Chemical Society
Ind. Eng. Chem. Res., Vol. 33, No. 11,1994 2669 (Hustedt et al., 1989; Kula et al., 1982), and (i)technology assessments (Fair, 1989; Michaels, 1992). Recently, a 2-day symposium on aqueous biphasic separations, covering 35 papers from biomoleucles to metal ions, was held at the American Chemical Society National Meeting in San Diego, CA, April 1994. Recent fundamental research has led to four key classes of theoretical models for protein partitioning in ATPS: (1)adsorption models based on thermodynamics of adsorption of polymers from dilute solution to spherical solid particles (Baskir et al., 1987; Baskir and Hatton, 1989); (2) Ogston-based models utilizing the osmotic virial equation for thermodynamics of dilute aqueous mixtures (e.g., Forciniti and Hall 1990; King et al., 1988); (3)Flory-Huggins-based models applying the Flory-Huggins equation of state for polymersolution thermodynamics (e.g., Diamond, 1990; Diamond and Hsu, 1990); (4)perturbation models based on statistical-mechanical calculations considering the protein shapes (e.g., Haynes et al., 1993; Mahaderan and Hall, 1990, 1992). After introducing some background on expert networks in the following section, we shall describe in section 4 the motivation for and the advantages and limitations of our neural network models when compared to available theoretical models for protein partitioning in ATPS.
Input Data
Neural Network
(Nonnalizcd Vector)
Shell
Expert System Figure 2. Illustration of an expert network.
n
n
Output Layer Hidden Layer 3
Hidden Layer 2
Hidden Layer 1
3. Background on Expert Networks 3.1. Expert Systems. Chapter 10 of our textbook (Quantrille and Liu, 1991) introduces the fundamentals and applications of expert systems. Briefly, an expert system attempts to match the performance of human experts in a given field. To do so, the system relies on in-depth, expert knowledge. The better knowledge, the better is the performance of the system. Knowledge is usually incorporated into an expert system through relationships. An expert system keeps track of relations and inferences invoked. Therefore, the knowledge used by the system is explicit and accessible t o the user. An expert system can explain why certain information is needed, and how certain conclusions are reached. Two advantages of expert systems are that they (1) can assimilate large amounts of knowledge and (2) never forget that knowledge. These properties distinguish expert systems from conventional computer programs. Ideally, an expert system can build its own knowledge base, although achieving that goal has been very challenging. Another ideal is for field experts who are not programmers t o expand that knowledge. A typical expert system contains (1)a knowledge base, (2) an inference engine, and (3) a user interface. These three components are illustrated as the lower blocks in Figure 2. The knowledge base contains specific, indepth information about the problem a t hand. That knowledge consists of facts, rules, and heuristics. To utilize the knowledge, an expert system relies on its inference engine, which uses inference mechanisms t o process the knowledge and draw conclusions. The user interface provides a smooth communication between the program and the user. An expert system shell is simply the combination of the user interface and the inference engine. Ideally, the shell (1)answers how a conclusion was reached, (2) explains why certain information is needed, and (3) has the ability to add knowledge to the knowledge base. 3.2. Neural Networks. A neural network is a computing system consisting of a large number of
Classifier @am Strucnuing)
Input Layer
Figure 3. Generalized backpropagation network with feedforward prediction capability.
T:
x2
L
Figure 4. Anatomy of the j t h processing element that transfers the ith input zi to the jth output yj through a weighting factor wji and a transfer function flZ,). Tj is the internal threshold for processing element j.
processing elements (also called nodes or neurons) which process information by determining the values of output signals based on the values of input signals (HechtNielsen, 1990). Chapter 17 of our textbook (Quantrille and Liu, 1991) describes in detail the principles and practice of neural networks, including a comparison between neural network and empirical numerical modeling or curve-fitting. Figure 3 illustrates a frequently used network, called the generalized backpropagation network with feedforward prediction capability (Hecht-Nielsen, 1990; Rumelhart and McClelland, 1986). This network consists of three sections: input layer, hidden layers, and output layer. The input layer receives information from an external source, consisting of nodes of system parameters and operating variables that control the system response, The hidden layers are the driving force of the neural network. There are normally one to three hidden layers of multiple nodes which perform the system calculations. The number of hidden layers depends on the nonlinearity of the system and the extent of the
2670 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 Table 1. Neural Networks versus Expert Systems (Samdani, 1990) ~
Subnet 1
Subnet 2
subnet 3
Figure 5. Hierarchical neural network architecture
variable interactions. The output layer receives the processed information from the neural network and sends the response to an external receptor. The nodes or neurons of the hidden layer(s) are the processing elements, as illustrated in Figure 4. Thejth processing element transfers the ith input variable, xi, to the j t h output variable, yj, through a weighting factor wji, an internal threshold value for the processing element, T,, and a transfer function of the sum of all weighted input variables to the element minus the internal threshold, fcl,), where l, = Cwjix, - 5'). The three most frequently used transfer functions are 1. sigmoid function:
2. sine function:
1 f(lj) =1 e-']
+
PIj) = sin(lj)
3. hyperbolic tangent function:
To develop a neural network model, we use two groups of input-output data, one to train the network and the other to check for generalization. In neural network development, training refers to the initial phase in which we repeatedly present sets of inputoutput data to the network and adjust the weights of the interconnections to minimize error. Generalization corresponds to the final phase where we feed new input data to the network. Hopefully, with the training the network has undergone, the output response will be proper. One specific type of backpropagation network used in our bioseparation predictor is the hierarchical network (Hecht-Nielsen, 1990; Mavrovouniotis and Chang, 19921, as shown in Figure 5. This architecture has several layers segmented into subnetworks, where the input vectors are divided into property groupings. This structure allows for the processing of data in stages where the effects of independent variables are compartmentalized into their own sectors. As the network progresses into the upper hidden layer, higher-order interactions are taken into account. Each of the subnetworks is expected to summarize in its outputs the important features of the selected subset of inputs. Note that the key operating variables can be included in multiple subnetworks when required. The outputs of the first layer of subnetworks from an internal representation being used by the subnetworks at the next level to model larger sets of inputs a t a higher level. There are several advantages to using a hierarchical architecture (Mavrovouniotisand Chang, 1992). First, more processing elements are used with fewer interconnecting weights, thus improving the efficiency of the network. Therefore, the network can be trained with a
neural networks example-based domain-free find rules little programming easy to maintain fault tolerant need a database fuzzy logic adaptive system
~~
~
~
~~
~~
expert systems rule-based domain-specific need rules much programming difficult to maintain not fault tolerant need a human expert rigid logic require programming
fewer number of examples and with a shorter training time. For complex systems, well-defined subnetworks of related variables provide hints that help the network learn in the right direction. The layout is also much more structured, giving greater understanding to the user of what is occurring in the system. The individual subnetworks can be analyzed in order to decipher what the different segments of the network have learned and can be mapped to certain rules regarding the quantitative effects of different independent variables. We should emphasize that because of this learning ability of a hierarchical network, our neural network modeling of reported experimental data is definitely not a task of empirical data correlation. 3.3. Expert Networks. Although expert systems and neural networks are two important techniques of artificial intelligence, they have little in common. Table 1 compares how both techniques function (Samdani, 1990). When an expert system and a neural network are combined to form an expert network, they complement each other to compensate for the other's weakness. Figure 2 illustrates one approach to placing a neural network in series with an expert system. Data representing the independent variables of a given system serve as the input to a previously trained neural network. The neural network predicts the desired response variables, usually in the form of a numerical value. The numerical response values must be converted into categorical data (eg., 0 = poor; 1 = average; or 2 = good) in order for the expert system to use the information. Ocassionally, by using certain types of probabilistic classification networks (Neuralware, 19931, the output will already be in the format required by the expert system and the classifier is not needed. The fuzzy data obtained from the neural network and classifier can then be subjected to the rules and heuristics of the expert system to identify optimal operating conditions. 4. Comparison of Neural Network Models to Available Theoretical Models for Protein Partitioning 4.1. Advantages and Limitations of Neural Network Models. Neural networks should primarily be used to complement the theoretical models in designing an effective strategy to facilitate experimental design and process development. The theoretical models have the ability to describe the behavioral patterns of a given system and to show the basic trends that the system will follow. In comparison, neural network models store the patterned behavior within its interior structure which is hidden to the user. Consequently, this leaves the user with limited information about the solution's validity. However, the neural network does have the ability to recognize more complex response patterns than corresponding empirical models, especially when there is a large set of independent variables that
Ind. Eng. Chem. Res., Vol. 33,No. 11, 1994 2671 influence the solution. The advantages and limitations of neural computing applied to protein partitioning are listed below. Ad vantages: 1. The neural network model recognizes patterned behavior without regard to mathematical complexity. 2. The neural network model allows for the inclusion of an expanded set of input variables, for example, the use of the polydispersity index for the polymers (Connemann et al., 1992) and the use of hydrophobicity term for the protein (Albertsson, 19861, which are thought to have a significant impact on how a protein will partition between phases. 3. The neural network model uses the protein properties predicted by amino acid compositions and protein molecular weights in conjunction with polymer-solution and ion properties to account for all binary interactions. The approach eliminates the need for tedious experimental measurements and data correlation required by most theoretical models for the estimations of interaction parameters (a) between protein and polymer (e.g., by fitting the Gibbs free-energy equation t o solubility data for the protein in an aqueous solution with the specified polymer), (b) between polymer and polymer (e.g., by using low-angle light scattering data), and (c) between ion and polymer (e.g., by fitting the Gibbs freeenergy equation to osmotic-pressure data for ternary aqueous solutions of polymer and the salt of the ion) (Haynes et al., 1989). 4. New sets of experimental data from future research, that do not follow historical predicted behavior of the system, can readily be added to the model, thus improving the future prediction capabilities. 5. Compartmental neural network structures permit easy incorporation of new independent variables. For example, when the prediction of the tertiary structure for a protein becomes available, the additional input variables can be inserted into the network structure with minimal effort. 6. The network is well suited t o handle noisy, incomplete, or inconsistent data. The network is able to filter data because each processing element affects the input-output pattern only slightly. Since each processing element operates relatively independently of the other elements, the network has significant parallel processing capabilities (Quantrille and Liu, 1991, pp 442-445). Limitations: 1. There is no theoretical foundation behind the neural network model. Therefore, the neural network model does not provide the user with explicit reasoning behind its solution, and we may need to use some insights from theoretical models to support and validate the neural network solution. 2. It requires a broad set of training examples to build an effective neural network model. Predictions outside the boundaries defined in the training examples are often poorly estimated. Therefore, the development of a training database is required to be diverse, complete, and well-structured. As stated above, most theoretical models used for the prediction of protein partitioning are complex in nature and require the use of adjustable parameters, namely, the protein-polymer, polymer-polymer, and ionpolymer interaction parameters, to adequately describe the system. The interaction parameters are functions of many polymer-solution, protein, and ion properties. The neural network approach provides an alternative, but effective and flexible means for the user to incorporate all the properties that have sigdicant influences
(Null Network
curve-fitting
training
Figure 6. Comparison of theoretical thermodynamic models based on interaction parameters to a neural-network model for the prediction of partition coefficients.
Present location of network training
prediction of output variable
Number of Training Examples Figure 7. Typical learning curve for a neural network model.
on the interaction parameters into the model (see Figure 6). Therefore, we can predict how a protein will partition into the two aqueous phases without requiring considerable experimentation and curve-fitting to obtain the measured interaction parameters. We stress again that a major limitation of neural computing is its requirement for a large and diverse set of examples needed to train the network. This is especially difficult for the complex problem of protein partitioning in ATPs where there are thousands of proteins having large variations in functions and properties, and five other key independent variables ( ~ ~ W P E G , hfwdextran, % PEG, % dextran, and pH). As will be shown in section 6.6, over 1000 experimental systems are used to train the network, yet only 5 proteins are included in this study, for which there are extensive data on their partitioning behavior. Figure 7 shows a typical learning curve for a neural network model in which we identify the amount of information presently available for training the network and the threshold point where the network becomes a very effective tool for pattern recognition. With the network still in the early region of the learning curve, the network is only capable of fuzzy inferences into how the protein will partition. However, fuzzy inferences can still be used as an effective tool to facilitate experimental design and process development. As the experimental data in this field begin t o grow, the neural network predictor will become much more reliable and effective. Considering that there are thousands of proteins, we believe that this type of model can be very useful in directing experimental design and process development while all of the protein interactions are being quantified. 4.2. An Illustrative Example Showing Effects of Protein Properties. An example provided by Forciniti and Hall (1991) demonstrates how protein properties can have significant effects on partitioning behavior in ATPs and reveals some of the limitations of most theoretical models. In this case, we consider the partition coefficients for five proteins as a function of the tieline length, as shown in Figure 8.
2672 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 10
1
i
Chymotrypsinogen-A
Optimizer (ExpenSystem)
Controllcr (Expert System)
Bioscparation Predictor (Neural Network)
Optimizer (Response-Surface Model)
Figure 10. Proposed approach to predictive modeling and optimal design of extractive bioseparations.
Tie-Line Length
Figure 8. Comparison of partition coefficients for five proteins as a function of tie-line length (Forciniti, 1991).
greater detail how protein properties will influence partitioning behavior. 5. Overview of the Research Approach
Free Free Energy Energy (kcallmole) (kcallmole)
- - " - 4 8
-8 2 - 8 8 - .. 9,
Hydrophillic
.I2
Figure 9. Hydrophobicity distribution for chymotrypsinogen-A and lysozyme. Table 2. Comparison of Basic Protein Properties for the Five Proteins Used in Figure 8 ~~
protein lysozyme chymotrypsinogen-A bovine serum albumin transferrin catalase
molecular weight 13 200 23 200 65 000 73 000 250 000
isoelectric point 10.5-11.0 9.5 4.7 5.2 5.6
A general trend for most of the thermodynamic models indicates a decreasing partition coefficient as the molecular weight of the protein increases. As seen in Figure 8 and Table 2, the trend is generally followed except that lysozyme and chymotrypsinogen-A are interchanged in order. There are two main explanations for this deviation: (1)lysozyme interacts preferentially with dextran, or chymotrypsinogen-Ainteracts preferentially with PEG; and (2) lysozyme self-associates t o form a dimer or trimer, resulting in a higher apparent molecular weight. Both explanations lead to the conclusion that a protein's properties can play a significant role in its partitioning behavior. Figure 9 shows a distribution of the amino acids that make up each protein listed in order of their hydrophobicity (from hydrophobic t o hydrophilic). As seen by the distribution, chymotrypsinogen-Ais more hydrophobic in nature than lysozyme, which can lead to an affinity toward the one phase. This type of preferential partitioning will become much more significant as the pH of solution deviates from the isoelectric point of the protein. This example demonstrates that a protein's physical and structural properties can have a significant impact on how it will partition between phases. Albertsson (1986, pp 56-71) and Forciniti (1991) both describe in
Figure 10 shows an overview of our approach to the predictive modeling and optimal design of extractive bioseparations in ATPs, which can be applied to protein purification (Baughman and Liu, 1993, 1994). This approach uses the qualitative reasoning skills of an extractive-separation expert system as a central controller for overall processing control and as a process optimizer for selecting best extractor designs (Brunet and Liu, 1993). It utilizes the quantitative modeling capabilities of a protein-partitioning network as a bioseparation predictor for selecting the best multiphase-forming polymer/salt systems and the biospecific affinity ligands and for specifying the optimal ranges of independent variables, and for diagnosing a fault map of fault regions where independent variables correspond to destructive environments (e.g., denaturation) for protein partitioning. In addition, the strategy incorporates a bioseparation optimizer that applies the responsesurface model to identify the optimum values of key independent variables t o assist in experimental design and process development.
6. Bioseparation Predictor: Protein-Partitioning Network 6.1. Partition Coefficients of Proteins in Aqueous Two-PhaseSystems. We wish to develop a neural network model to quantitatively predict the partition coefficients (i.e., separation factors), Kp, of proteins in ATPs over wide ranges of independent variables, such as protein properties, polymer-solution properties, and ion properties. Albertsson (1986, pp 56-71) presents a detailed overview of the factors that determine how a protein will partition between phases, including sizedependent, electrochemical, hydrophobic, biospecific, and conformation-dependent contributions. The logarithm of the overall partition coefficient is then represented as a linear combination of the logarithm of each of these contributing factors. We use a similar form of Albertsson's equation to represent the logarithm of the partition coefficient, except that we include the hydrophobic and conformation-dependentproperties as input variables within our neural network structure. Our overall equation to predict the partition coefficient is
l n K p = l n K , + l n K p H + l n K t + l n K e + l n K b ... + where K, = partition coefficient of the polymer solution at standard conditions (temperature at 25 "C and pH at the isoelectric point), K P=~partition contribution due to pH variation from the isoelectric point, Kt = partition
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2673
L I
Hidden Layer 3
**F, Hidden Layu 1
I
Table 3. Specificationsfor the Protein-Partitioning, Polymer-Solution, and Property-Property Networks network type backpropagation training file name &x.nna, peggnna, inttns .nna , ahelix. nna , bsheetana, part.nna, phpart.nna transfer function (input layer) linear transfer function (hidden layers) tanh transfer function (output layer) tanh delta rule learning rule summation sum error standard network weight distribution normal distribution: 3 u limits of [-1, 11 Input Layer
Poiymer Solumn Ropatlm
- temperahue
-c o m p m n
-Mw PEG -Mw Dextran
- interfaaal t m o n -- APEG AbIeam
PropClt1es
- mlecularwght ~soclectncpomt (Ip) - % a - h&x ~
B -sheet - hmh&Iflty -%
-
net charge -pK pMlal speclfic volume
Prcrpertles
- sohltm psr w -IP) - salt mcentrauon - Ion dsmeter
- im hydnnon nlrmber - ion-ion specific intcractmn
training iteration noise learning rate momentum coefficient error tolerance
contribution due to the temperature variation from 25 "C,K, = partition contribution from electrophoresis, and Kb = partition contribution from affinity binding. The logarithmic form of this equation gives us the flexibility of incorporating additional contributing terms to reflect the effects of new independent variables that result from future experimental findings. 6.2. Architecture of the Protein-Partitioning Network. We combine the best features of both Figures 3 and 5 t o give the architecture of the proteinpartitioning network, Figure 11. The architecture consists of three subnetworks, with their input nodes corresponding to three groups of properties that affect protein partitioning in ATPs (Baskir and Hatton, 1989; King, 19921, namely, (1)polymer-solution properties, (2) protein properties, and (3) ion properties. Hidden layer 1 represents the interactions within each of the subnetworks, while hidden layers 2 and 3 account for higher-order interactions between the groups. As shown in Figure 11,the polymer-solution properties include the major variables from both the Ogstonbased models (e.g., Forciniti, 1991; Forciniti and Hall, 1990; King et al., 1988) and Flory-Huggins-based models (e.g., Diamond, 1990; Diamond and Hsu, 1990). Specifically, they are temperature, compositions, molecular weights MWPEG and MWdextran, gradients of PEG and dextran concentrations between the partitioned phases (i.e., APEG and Adextran), and interfacial tension. The protein properties included in Figure 11are to be discussed later in section 6.4, Protein-Property Network. The ion properties are present in the Ogstonbased models (e.g., Forciniti and Hall, 1990; King et al., 1988) as an electrostatic potential term. Here, we select solution pH and the variation from the isoelectric point as two main independent variables. We also consider salt properties that include salt concentration, ion diameter, ion hydration number, and ion-specific interaction coefficient. The ion properties will be further discussed in section 6.5. Table 3 shows the primary specifications used in training the polymer-solution, protein-property, and protein-partitioning networks. We use a standard backpropagation network with three hidden layers. The hyperbolic tangent transfer function, tanh, is found to be effective for this problem and is recommended for
0.9 0.6 0.0
Hidden Layer 1
Coeffia&
Figure 11. Protein-partitioning network
5 000 0.0
training iteration noise learning rate momentum coefficient error tolerance
10000 0.0
30000
0.3
0.15 0.20 0.1
0.4 0.1
0.0
70000 0.0 0.0375 0.05 0.1
Hidden Layer 2 training iteration noise learning rate momentum coefficient error tolerance
10000 0.0 0.25 0.4
0.1
30000 0.0
0.125 0.20 0.1
70000 0.0 0.03125 0.05 0.1
Hidden Layer 3 training iteration noise learning rate momentum coefficient error tolerance
10000 0.0
0.2 0.4
0.1
30000 0.0 0.1 0.20 0.1
70000 0.0 0.025 0.05 0.1 70000 0.0 0.01875 0.05 0.1
Output Layer training iteration noise learning rate momentum coefficient error tolerance
10000
30000
0.0
0.0
0.15
0.075 0.20 0.1
0.4 0.1
prediction networks. We use the delta rule (Quantrille and Liu, 1991, pp 457-462) for training this network, but many of the other learning rules can be used without any loss in effectiveness. The normal distribution of network interconnecting weights is set at a standard level having 3 (T (standard deviation) limits of -1 t o +l. Table 3 also shows how the noise, learning rate, momentum coefficient, and error tolerance are adjusted at different iterations of the training process for the input and output layers, and each of the three hidden layers (Neuralware, 1993). 6.3. Polymer-Solution Network. A. Architecture of the Polymer-Solution Network. We use the polymer-solution network of Figure 12 to accomplish two tasks: (1)to obtain the required, polymer-dependent, input variables for the protein-partitioning network of Figure 11, particularly the concentration gradients (APEG and Adextran) and interfacial tension; (2) to generate phase diagrams for user reference, indicating quantitatively how the aqueous PEG/dextran solution splits into two phases. As shown in Figure 12, four groups of properties contribute to how the two phases form, namely, (1) polymer-solution interactions, (2) polymer properties, (3)compositions, and (4) temperature.
2674 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
Yo PEG
% Dextran
Bottom
TOP
A612 A61S
A62s
Interfacial Tension
Mw : PEG Mw : Dextran PI : PEG PI : Dextran
A PEG
A Dextran
-
% PEG (Total) YODextran (Total) In (%Dextran*%PEG) %Dextran / %PEG
Figure 12. Polymer-solution network.
The polymer-solution interactions are accounted for by using the solubility-parameter differences, 812, 81a, and 8za (1, PEG; 2, dextran; s, solvent). Since we consider only the PEGIdextranJwater system, these solubility parameters are constant and the corresponding network interconnections have an essentially identical effect on the output-response patterns. We note that the prediction of solubility parameters for glucose-based polymers, such as dextran, by group-contribution methods have problems in accurately representing variances in separations. In future work, when multiple-phase systems are included, interaction properties will need to be better defined (Barton, 1983). The polymer properties in Figure 12 consist of not only the molecular weights (MWPEGand M d e x t r a n ) , but also the polydispersity index (PI), which is the ratio of the weight-average molecular weight M , to the numberaveraged molecular weight Mn. A recent study (Connemann et al., 1992)has shown that the polydispersity index must be included in any model to accurately predict the partitioned phase behavior in ATPS. We note that both Ogston and Flory-Huggins models fail to account for the molecular-weight distribution of dextran. The compositions in Figure 12 include the weight percents of PEG and dextran, and ln(%PEG x %dextran). The latter logarithmic term represents an interaction term for compositions that we have found t o be very effective. B. Illustrative Predictions by the PolymerSolution Network. We train and test our network using 22 phase diagrams, including 64 training examples from Forciniti (1991) and Forciniti and Hall (1990),32training examples from Diamond (19901, and 20 training examples from Albertsson (1986). These data are divided into two sets, one to train the network, and the other to check for generalization. We randomly select 22 data points as the generalization set for the interfacial tension, APEG, and Adextran subnetworks in Figure 12. The predictions for the %PEG in the bottom phase and the %dextran in the top phase are trained with the complete data set. This is done since
Table 4. Format of the Files dex.nna, dextp.nna, peg.nna, pegbot.nna, and inttns.nna Used for Training the Polymer-Solution Network column variable no. type 1 input 2 input 3 input 4 input 5 input 6 input 7 input 8 input 9 input 10 input 11 input 12
13a 13b 13c 13d 13e
input output output output output output
normalized variable A&z2 A6zS2 MWPEG PIPEG MWdextran PIdextran %PEG %dextran %dextranl%PEG ln(%dextran x %PEG/100) T - Tstandard Adextran %dextranb, APEG %PE@,tb, interfacial tension
normalization factor
file name
100 10 000 10 000 100 000
10 1 000 000 10 100% 100%
2 1 dex.nna dexbot.nna pegnna pegbotnna inttnsnna
50 "C 100% 100%
1008 100% 1000 pN
they are only required for the presentation of the ternary diagram and not for use in the proteinpartitioning network of Figure 11. The data are presented to be network in 13 columns, 12 input and 1 output. Table 4 shows the format of the data files dex.nna, dextop.nna, peg.nna, pegbot.nna, and inttns.nna used in the training and testing of the polymer-solution network (all data files in this work are available to the reader upon request). Table 5 specifies the molecular weights and polydispersity-index (PI) values used in our database. We apply a very efficient and user-friendly, PC-based software, Neuralworks Professional 11, Neuralware, Inc., Pittsburgh, in our computations. Table 6 gives the correlation coefficients for predictions by the APEG, Adextran, and interfacial tension subnetworks of Figure 12. Figure 13 shows the scatter plots of the predicted versus experimental values, and Figure 14 presents examples of comparison of predicted and experimental phase diagrams. As seen, the major-
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2676 Table 5. Specifications of PEG and Dextran for the Illustrative Predictions by the Polymer-Solution Network M" PEG 3400 PEG 4000 PEG 6000 PEG 8000 PEG 10000 PEG 20000 dextran 10000 (D17) dextran 40000 (D19) dextran 70000 (D24) dextran 110000 (D37) dextran 500000 (D48)
M,
3 400
3400
4 100 5 600
4 100
8 000 11400 21 000 23 000 20 000 72000 83000 180 000
8 000 11400 21000 30000 42000 135000 179000 460 000
5 600
a 30
training generalization combined
training generalization combined
data points 52 12 64
T
PI
1.00 1.00 1.00 1.00 1.00 1.00 1.30 2.10 1.88 2.16 2.55
Y
3
-
0 0
Table 6. Correlation Coefficients for Illustrative Predictions by the Polymer-SolutionNetwork data points 96 25 121
A Dextran Prediction Scatter Plot
correln coeff APEG Adextran 0.9902 0.9949 0.9871 0.9607 0.9940 0.9818
COOH
I
NH- C-H I
PI
The properties of the residue groups in conjunction with their structural position define the solution properties
15
10
20
25
30
Actual Value
A PEG Prediction
b
correln coeff interfacial tension 0.9964 0.9728 0.9937
ity of prediction errors in the phase diagrams appears in the low APEG and Adextran regions near the plait point. This is consistent with results from other techniques such as the Flory-Huggins model. For extraction applications, these regions are generally not feasible operating conditions. Therefore, the observed prediction errors are of little practical significance. The fact that the correlation coefficients in Table 6 are very close to unity indicates that the polymer-solution network of Figure 12 can accurately predict the required polymer-dependent input variables for the proteinpartitioning network of Figure 11. 6.4. Protein-Property Network. A. Independent Variables and Architecture for the ProteinProperty Network. The protein properties are included in the protein-partitioning network to account for the protein's affinity toward a specific phase. The top phase consists predominantly of the hydrophobic polymer, P E G the bottom phase consists primarily of the glucose-based polymer, dextran. The differences in physical properties between these two polymers and their interactions with the protein determine how the protein will partition between the two phases. Therefore, it is desirable to incorporate additional protein properties, such as hydrophobicity and secondary structure, to represent the polymer-protein interactions and effectively train the network. As discussed in section 4.2, these properties are accounted for by the experimentally measured interaction parameters used in the statistical thermodynamic models. Proteins are complex polymers composed of a series of amino acids attached by peptide bonds. There are 20 different naturally occurring amino acids present in proteins, each with a different residual group, [Rl:
5
Scatter Plot 16
4 0
0
4
8
12
16
20
Actual V a l u e
T
Interfacial Tension Prediction Scatter Plot
0
5 0 100 150 200 250 300 3 5 0
C 350
300
Y
250
?
200
1
150
B
100
50 0 Aotual Value
Figure 13. Scatter plots of predictions by the polymer-solution network ( 0 )generalization; (0)training results. Data sources: Albertsson (19861, Diamond (1990), and Forciniti (1991).
of the protein. The amino acids can be categorized into five groups: aliphatic, nonpolar, aromatic, polar, and charged. Table 7 shows the 20 amino acids listed in order of ascending hydrophobicity, measured on the basis of solubility in various solvents (Branden and Tooze, 1991). There are four structural groupings for proteins, as shown in Figure 15. The primary structure is the amino acid sequence of a polypeptide chain. The secondary structure is the conformational of the backbone such as a-helix or ,!?-sheet. The tertiary structure is the threedimensional conformation, representing how the secondary structure folds in order to obtain the most
2676 Ind. Eng. Chem. Res., Vol. 33, No. 11,1994
a
h h a r n f c . D n m s i P E ~ PEG 1om . -Damn ll0,om
1
20.0
16.0
Table 7. Amino Acid Characteristics (Brandon and Tooze, 1991) free energy residue amino acid (kcallmol) category 3.7 aromatic Phe phenylalanine 3.4 nonpolar Met methionine 3.1 aliphatic Ile isoleucine 2.8 aliphatic Leu leucine 2.6 aliphatic Val valine 2.0 nonpolar Cys cysteine 1.9 aromatic Trp tryptophan 1.6 aliohatic Ala alanine 1.2 polar Thr threonine 1.0 nonpolar Gly glycine 0.6 polar Ser serine -0.2 nonpolar Pro proline -0.7 aromatic Tyr tyrosine -3.0 aromatic His histidine -4.1 polar Gln glutamine -4.8 polar Asn asparagine -8.2 charged (-) Glu glutamic acid -8.8 charged (+) Lys lysine -9.2 charged (-1 Asp aspartic acid -12.3 charged (+I Arg arginine ~~
0.0
5.0
10.0
15.0
20.0
25.0
30.0
9 % -
e h a r c m h r W E S m
b
m2o.m - Damn l0,om 20.0 16.0
/A
0.0
C
0.0
5.0
10.0
15.0
25.0
20.0
30.
%KEnrm
Figure 14. Comparison of experimental phase diagrams with
.
neural network oredidions: (0)oredicted, (0) . . exoerimental. Data sources: (a) Fbreiniti (1991j,'(b) Albertsson (1986), and (e) Diamond (1990).
favorable thermodynamic state with hydrophobic residues in the interior and hydrophilic residues on the Serandary
exterior. The quaternary structure is the arrangement of aggregation of several polypeptide chains. There are two thermodynamically favorable conformations for polypeptide chains, the a-helix and 8-sheet structures (Figures 16 and 17). The a-helix is a tight coil with 3.6 amino acids per turn. The helix is stabilized by hydrogen bonds between NH and the CO groups. All hydrogen bonds in the a-helix are pointed in the same direction, NH pointing toward the Nterminal side and CO pointing toward the C-terminal side. The polarity differences between the CO and the NH groups cause an overall dipole moment along the helical axis. The most common position of the a-helix is at the surface of the protein, where one surface of the a-helix is hydrophobic and the other hydrophilic (Figure 16). The 8-sheet conformation is composed of amino acid strands, approximately 5-10 units in length, aligned adjacent to each other. The p-sheet structure exists in two forms, parallel and antiparallel (Figure 17). In the parallel form, all strands run in the same direction, while the strands alternate directions for the antiparallel form. Unlike the a-helix structure, both forms of the 8-sheet conformationhave alternating directions of the hydrogen bonds between the NH and CO. Therefore, there is no hydrophobidhydrophilic side at the surface of the protein, but hydrophobic and hydrophilic side chains will be staggered. This difference will cause variations in partitioning behavior between two differTertiary
J?..,
Y'
Figure 15. The four structural groups of proteins. Reprinted with permission from Branden and Tooze (19911, Zntroduction to Protein Structure. Copyright 1991 by Garland Publishing, New York.
Ind. Eng. Chem. Res., Vol. 33, No. 11,1994 2677 A
E
C
F
1
5A
-I
Figure 16. The a-helix secondary structures ofpmteins. Reprinted with permission from Stryer (19881,Biochemistry,3rd ed. Copyright 1988 by Lubert Stryer. Used with permission of W. H. Freeman and Company. Models of a right-handed a-helix [AI only the a-carbon atoms are shown on a helical thread; FBI only the backbone nitrogen (N), a-carbon (CA, and carbonyl carbon (C) atoms are shown; [Cl entire helix. Hydrogen bonds between NH and CO groups stabilize the helix.
Figure 17. The &sheet secondary structures of proteins. Reprinted with permission fromStryer (1988),Biochemistry, 3rd ed. Copyright 1988 by Lubert Stryer. Used with permission of W. H. Freeman and Company. Antiparallel B pleated sheet. Adjacent strands run in opposite directions. Hydrogen bonds between NH and CO groups of adjacent strands stabilize the structure. The side chains are above and below the above the sheet.
ent proteins that have varying secondary structures. Therefore, knowledge of the secondary structure is important in predicting the protein's partitioning behavior in ATPs. We note that there are also linear and @-turnregions in the secondary structure. These regions have less effect on the partitioning variations and are indirectly considered as dependent variables. In addition to the structural effects of proteins on the partitioning behavior, there are other protein properties
that influence the protein's partitioning behavior. We select the protein's hydrophobicity, bulk (size), specific volume, and pK, to include in our model. We also adopt some of the results from the significant work of Kidera et al. (1985a,b). As seen in Figure 18, Kidera et al. statistically identified 188properties of amino acids that affect protein conformation and other physical properties. Two sets of cluster analysis were conducted to combine those variables having similar effects on protein properties. A principal-component analysis then
2678 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
+
188 Physiyl Properties
statistical test
+
116 physical properties
I
hierarchical cluster analysi 13
42 i
bulk
I!
hydrophobicity & p- structure
13
' bend structure
I
a -helix
II
K - mean cluster analvsis
111111
37
I I
t
I
statistical and correlation test I
1 ' 7 -
11 4 3 16 6 j ii i b HHHHHHHHH
16 physical properties
I 9 characteristic (average) properties
factor analysis (second step)
Figure 18. Kidera's statistical approach to identifying characteristic properties and characteristic factors for 20 naturally occurring amino acids (adopted from Kidera et al., 1985).
resulted in the following five groups of nine characteristic properties accounting for 68% variance of the original property set: 1, bulk; 2-4, hydrophobicity; 5, 6, a-structure preference; 7, P-sheet preference; 8, 9, bend preference. We only describe here the hydrophobicity characteristic properties (2-4) that are used in our proteinproperty subnetwork. These hydrophobicity properties are categorized into three independent groups. The first two groups are based on charged amino acids (arginine, asparagine, glutamine, and lysine). The amino acid will either suppress or include ionizable side-chain groups. The last hydrophobicity parameter is defined as the depth into which the amino acid is buried inside the three-dimensional structure of the protein. Table 8 gives values of Kidera's 9 characteristic properties for 20 naturally occurring amino acids (Kidera et al., 1985a). As seen in Figure 18, an additional factor analysis generated 10 orthogonal parameters, called characteristic factors, from the 9 characteristic properties and 16 other physical properties not included in the principal component analysis. This factor analysis increased the properties accounted for to 85%. The resulting 10 characteristic factors are 1, a-helix or bend-structure preference-related; 2, bulk-related; 3, p-structure preference-related; 4, hydrophobicity; 5, normalized frequency of double bond; 6, average value of partial specific volume; 7, a mixture of several physical properties; 8, normalized frequency in a-region; 9, pKc; 10, surrounding hydrophobicity.
I I
hddenLayer3 HiddenLayer2
!
=I
I II , I
l Kidera Vector Transformatlon .
l
1 I
Hidden Layer 1
20 Anuno-Acid Composihons and Protem-Cham Length
I
Figure 19. The protein-property network.
Table 8 gives values of the 10 characteristic factors for 20 naturally occurring amino acids (Kidera et al., 1985a). We use the following five Kidera parameters as independent variables that are not readily available for many proteins and cannot be easily predicted with accuracy: three hydrophobicity terms from the nine characteristic properties, pK,, and partial specific volume from the ten characteristic factors. Figure 19 shows the architecture of our proteinproperty network. The secondary structure percentages of a-helix and @-sheetfor proteins are predicted using a backpropagation network, while the Kidera parameters are calculated as the linear combination of amino acid compositions with their respective amino acid weighting factors.
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2679 Table 8. Kidera’s (a) Nine Characteristic Properties and (b) Ten Characteristic Factors for the Twenty Naturally Occurring Amino Acids (Kidera et al., 1986) amino acid
1
Ala Arg Asn Asp CYS Gln Glu GlY His Ile Leu LYS Met Phe
-1.44 1.16 -0.34
Pro Ser Thr RP Tyr Val
-0.54
-0.75 0.22 0.17 -2.16 0.52 0.21 0.25 0.68 0.44 1.09 -0.71 -1.21 -0.67 2.08 1.34 -0.34
amino acid
1
Ala Arg Asn ASP CYS Gln Glu GlY His Ile Leu LYS Met Phe Pro Ser Thr Trp Tyr Val
-1.56 0.22 1.14 0.58 0.12 -0.47 -1.45 1.46 -0.41 -0.73 -1.04 -0.34 - 1.40 -0.21 2.06 0.81 0.26 0.30 1.38 -0.74
2 -0.47 -0.57 -1.25 -0.75 0.06 -1.24 -0.62 -1.02 -0.46 1.37 1.06 -0.16 0.20 1.46 0.90 -1.19 -0.97 2.06 1.16 0.42 2 -1.67 1.27 -0.07 -0.22 -0.89 0.24 0.19 -1.96 0.52 -0.16 0.00 0.82 0.18 0.98 -0.33 -1.08 -0.70 2.10 1.48 -0.71
(a) Characteristic Property Number 3 4 5 0.32 -0.51 0.11 -0.28 -1.52 -1.07 -1.00 -0.60 -0.96 -1.74 -1.07 -1.17 0.63 1.50 0.60 0.19 -0.46 -1.05 -1.65 -1.03 -1.74 -0.19 -0.03 -0.84 -0.13 -0.56 -0.18 1.52 1.91 0.97 0.69 1.01 1.14 -0.86 -1.62 -1.76 0.72 1.00 0.45 1.24 1.16 0.88 -0.72 -1.26 0.21 -0.54 -0.33 -0.46 0.57 0.01 -0.36 1.55 0.67 0.61 1.04 -0.07 1.02 0.77 1.38 1.84
3 -0.97 1.27 -0.07 -0.22 -0.89 0.24 0.19 -1.96 0.52 -0.16 0.00 0.82 0.18 0.98 -0.33 -1.08 -0.70 2.10 1.48 2.04
(b) Characteristic Factor Number 4 5 6 -0.27 -0.78 -0.93 1.87 -1.70 0.46 0.81 0.18 0.37 0.81 -0.92 0.15 -1.05 -0.71 2.41 1.10 1.10 0.59 1.17 -1.31 0.40 -0.11 -0.16 0.10 1.01 0.28 1.61 -0.77 -0.54 0.03 -1.10 -0.55 -2.05 -1.62 1.70 1.54 1.52 -0.73 2.00 -0.81 -1.43 0.22 -0.45 -0.75 0.88 -0.43 0.42 -0.21 0.21 0.63 -0.10 -1.16 0.57 -1.57 -0.68 -0.56 -0.00 0.50 -0.81 -0.40
The tertiary and quaternary conformational effects on partitioning are indirectly considered in the interstructure of the protein-partitioning network (Figure 111, since many of the factors that influence these conformations are also factors in the protein-property subnetwork. B. Illustrative Predictions by the ProteinProperty Network. We train and test the network for secondary structure prediction (Figure 19)using 139 protein structures for training and 15 protein structures for testing the network which are obtained from Chou and Fasman (1974a,b)and Muskal(1991). The data are presented to the network in 22 columns, 21 input and 1 output variables. Table 9 shows the format of the training files ahelixnna and bsheet.nna, used for the training of the protein-property network. We have confirmed the finding of Muskal(1991)that the neural network approach predicts the secondary structure more accurately then the previously developed models, such as the probabilistic and multiple linear regression methods which can only achieve a 66% prediction level. Figure 20 and Table 10 show the prediction capabilities of percent a-helix and percent @-sheet.Note that the protein-property network is still in its early stage of development and should only be used for proteins that do not have their secondary structure defined in the currently available protein data
6 -0.86 -0.13 -1.19 -1.72 1.14 -0.42 -1.78 -0.99 -0.10 1.27 0.02 -1.19 0.24 0.48 0.86 0.22 0.86 0.42 1.21 1.66 7 -0.20 0.92 -0.09 -1.52 1.52 0.84 0.04 1.32 -1.85 -0.83 0.96 1.15 0.26 0.67 0.30 -1.89 0.24 -0.48 -0.31 -1.07
7 1.35 -0.16 -0.97 -0.06 -0.53 0.57 1.96 -1.72 0.59 0.06 0.93 0.71 1.39 0.37 -1.72 -0.99 -0.68 0.23 -1.25 -0.09
8 -1.29 0.28 1.19 0.74 1.18 -0.14 -1.21 1.43 -0.27 -1.30 -1.36 0.40 -1.24 -0.46 1.03 0.74 0.11 0.83 0.94 -1.63
8 -0.08 -0.39 1.23 0.47 -0.69 -0.71 0.38 2.36 0.47 0.51 -0.76 -0.08 0.11 1.10 -2.30 -1.15 -1.15 -0.40 1.03 0.06
9 -0.60 -0.03 1.27 1.39 -0.19 -0.12 -0.27 1.73 -0.27 -1.49 -1.14 0.15 -1.29 -0.75 1.98 1.02 0.14 -0.52 0.30 -1.32
9 0.21 0.23 1.10 0.76 1.13 -0.03 -0.35 -1.66 1.13 0.66 0.45 -0.48 -1.27 1.71 0.74 -0.97 -0.56 -2.30 -0.05 -0.46
10 -0.48 0.93 -1.73 0.70 1.10 -2.33 -0.12 0.46 1.63 -1.78 0.93 0.60 0.27 -0.44 -0.28 -0.23 0.19 -0.60 0.53 0.65
Table 9. Format of the Files a h k x . n n a and bsheet.nna Used for Training the Protein-Property Network no. of amino acids in the protein 1 no. of amino acids in the protein 2 input % alanine % arginine 3 input 4 input % asparagine 5 % aspartic acid input 6 input % cysteine % glutamic acid 7 input % glycine 9 input 10 input % histidine 11 input % isoleucine 12 input % leucine % lysine 13 input 14 input % methionine 15 % phenylalanine input 16 input % proline 17 input % serine 18 input % threonine 19 input % tryptophan 20 input % tyrosine % valine 21 input 22a output % a-helix 22b output % /3-sheet 1
input input
file name
normalization factor 1000
ahelix.nma bsheet.nna
100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
banks (e.g., from Brookhaven National Laboratory) or other reliable sources. Table 11gives values of the three
2680 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994
-
YOa Helix predictions
100.0
/
Scatter Plot A
8 P $
80.0
lysozyme
Y
r
40.0
P,
20.0
0.0 0.0
20.0
40.0
80.0
60.0
100.0
Actual Value (YO)
Scatter Plot
/ /
+
8 h
I
catalase
65 000 4.7
73000 250000 5.2 5.6
47.0 37.0 -0.130 0.121 -0.309
74.0 0.0 -0.250 0.036 -0.272
71.0 0.0 -0.142 0.113 -0.251
-0.074 -0.212 -0.106
-0.125 -0.142 -0.059
-0.101 -0.133 -0.126
Table 12. Anion and Cation Hard-Sphere Diameters in Dilute Aqueous Solutions at 25 "C (Haynes et al., 1993) cation Na+ K' Li+ Ca2+ Mn2+
YOp - Sheet Predictions
80.0
chymo- bovine trypsin- serum transogen-A albumin ferrin
molecular weight 13200 23200 isoelectric point 10.5 to 9.5 11.0 9% a-helix 53% 8.0 9% P-sheet 15% 40.0 bulk -0.141 -0.451 -0.014 -0.186 PKC specific volume -0.307 -0.274 hydrophobicity 1 (charge) -0.128 -0.220 -0.171 0.011 2 (charge) 3 (depth) -0.096 0.029
60.0
'0
3
Table 11. Specifications of Property Values for Five Proteins Used in the Illustrative Predictions by the Protein-Partitioning Network
dcation (A) 2.32 3.04 1.86 2.28 1.98
anion
c1HP04'HSO4-
so4-
danion (A) 3.62 4.44 3.82 3.66 3.28
Table 13. Hydration Numbers (h's)for Anions and Cations in Water at 25 "C (Ha.ynes, 1992)
60.0
U
cation
hcation
anion
hanmn
cs+
0.0 0.6 1.9 3.2 3.8 4.1 4.8
C104-
0.3 0.9 0.9 0.9 0.9 1.6 4.0
K' Na+ Li+ H+ Ca2+ Mg2+
B
-2 40.0
U
r
P,
20.0
c1-BrIRS03-
FOH-
Table 14. Ion-Ion Specific Interaction Coefficients,Bv, in Aqueous Solutions at 25 "C (Haynes et al., 1993)
0.0 0.0
20.0
40.0
60.0
80.0
100.0
Actual Value (YO) Figure 20. Scatter plots for secondary protein-structure predictions from the protein-property network. Table 10. Correlation Coefficients for Secondary Structure Prediction data points training generalization combined
139 15 154
correln coeff a-helix P-sheet 0.9966 0.8772 0.9885
0.9953 0.6958 0.9816
Kidera parameters for hydrophobicity as well as the percent a-helix and percent /3-sheet predicted by the protein-property network of Figure 20 for the five proteins, including lysozyme, chymotrypsinogen-A, bovine serum albumin, transferrin, and catalase. These independent variables serve as input variables for the protein-partitioning network of Figure 11. 6.5. Ion Properties. The effect of salts on protein partitioning is presently an area of intensive research. The ion properties have been the most difficult to model in regard to their effects on protein partitioning in ATPS. Haynes et al. (1993) have developed the most complete model, based on the osmotic virial expansion, which includes many additional electrostatic effects. This model is used as the primary source of our network parameters. We include the basic variables which do not require experimental measurements in our network structure. As more data become available on how the
electrolyte NaCl KCl NaH2P04
8,,
electrolyte
0.15
m2po4
0.10
NaHS04
-0.06
ms04
8,, -0.07 -0.07 -0.08
ion properties influence protein partitioning and as improved parameters are obtained for the representation of these properties, this subnetwork can be further developed. The salts added to the ATPs will partition unevenly between the two phases based on their chemical nature and their interaction with the two polymer phases. Uneven partitioning of the ions leads to an electrostaticpotential difference between the two phases, which causes the protein to partition preferably to one phase with a logarithmic correlation. The salt and ion properties used in the protein-partitioning network account for these effects. The first property that we introduce is the salt concentration. Albertsson (1986) shows how the addition of NaCl to an ATPs will reduce the partition coefficient of the protein. In order to use ion properties directly, we define the salt as a combination of an anion and a cation, e.g., NaCl is divided into Na+ and C1-. Both the anion and cation properties include the hardsphere diameter (Table 121, charge, and the hydration number (Table 13). We also include an ion-ion specific interaction coefficient (Table 14))/ 3 ~a t 25 "C, which is included in the model by Haynes et al. (1993). 6.6. Illustrative Predictions by the ProteinPartitioning Network. Having obtained all the
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2881 Table 15. Format of the Files purt.nna and phpurt.nna Used for Training the Protein-PartitioningNetwork column no.
variable type
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26a 26b
input input input input input input input input input input input input input input input input input input input input input input input input invut oitput output
normalized variable
file
normalization factor 1000 000 10 100% 100%
mpmtein
isoelectric point % a-helix % j3-sheet bulk parameter pKe parameter specific volume parameter hydrophobicity 1parameter hydrophobicity 2 parameter hydrophobicity 3 parameter pH - IP
1 1 1 1 1 1
10 100 000 1 000 000 100% 100% 1 100% 100% 1000 pN m-l 0.01 M 10 A 10 A 10 10
PEG
mdexkan
%PEG %dextran ln(%dextran x %PEG/100) APEG Adextran interfacial tension salt concentration cation diameter anion diameter cation hydration number anion hydration number ion-ion sDecific interaction coeff In K, In K P ~
required input variables for the protein-partitioning network of Figure 11,we test the training and generalization of the network using 295 data sets for In K, and 922 data sets for In K P(Forciniti, ~ 1991). The data are presented to the network in 26 columns, 25 input and 1 output variables. Table 15 shows the format of the datapart.nna andphpart.nna, used for the training of the protein-partitioning network. Figure 21a gives an example of the accurate predictions of the logarithm of the partition coefficient of the polymer solution at standard conditions (25 "C and pH at the isoelectric point), In K,. The network also performs well for the prediction of partition coefficient . due to pH variation from the isoelectric point, K p ~ As Figure 21b shows, the protein-partitioning network of Figure 11 works equally well. Table 16 shows the correlation coefficients for prediction by the proteinpartitioning network of Figure 11for both In K,and In K p ~ Again, . the correlation coefficients are very close to unit, indicating that the network can accurately predict both In K, and In K p ~ . The expanded set of protein properties used in our protein-partitioning network (Figure 11) is found to have minimal effects on the prediction of partition coefficients, In K,,when the pH is near the isoelectric point. The incorporation of the protein-property subnetwork becomes much more significant as the pH of solution deviates from the isoelectric point, Le., in the prediction of the partition coefficient, In KpH. The initial neural network architecture tested has only included molecular weight in the protein-property subnetwork, which is consistent with the variable sets from the Ogston and Flory-Huggins models. For the prediction of In K,, the prediction capability is very similar for both the initial and expanded protein-property subnetworks, with both achieving correlation coefficients of approximately 0.99. In comparison, the expanded set of variables in the protein-property subnetwork yields a significant increase in prediction capabilities of In K p ~ , improving the correlation coefficient from approximately 0.92 to 0.985.
1 1 1
part.nna phpart.nna
Protein Partitioning (In KJ Prediction Scatter Plot 5.0
-5.0
-4.0
-3.0
-2.0
T
1.0
2.0
3.0
4.0
5.0
Predicted Value
Actual Value
Protein Partitioning O S p H ) Prediction Scatter Plot
Actual Value
Figure 21. Illustrative predictions of protein-partitioning coefficients for polymer solutions a t standard conditions, In K,, and for variations from the isoelectric point, In K p ~ (0) : generalization; (0) training results. Data from Forciniti (1991).
2682 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 Table 17. Separation-Efficiency Classifier from Selectivity and Phase Classes phase-partitioning class selectivity poor medium good
Response-Surface Model
T
1
T
+,
I
Local Optimum for Each Set o f Primary Control Variables
very low poor medium high very high
infeasible infeasible infeasible poor poor
infeasible infeasible fair fair good
infeasible poor fair good very good
% Dextran
Figure 22. Response-surface modeling structure for determining optimal operating conditions of extractive bioseparations in ATPs of PEG and dextran. Table 16. Correlation Coefficients for Illustrative Predictions of Protein-PartitioningCoefficients for the Polymer Solutions at Standard Conditions, In K., and for , the Variations from the Isoelectric Point, In K p ~by Protein-PartitioningNeural Network of Figure 12
training generalization combined
data points
correln lnK,
235 60 295
0.994 0.992 0.994
data points 770 152 922
correln lnK,~ 0.991 0.967 0.988
7. Bioseparation and Process Optimizers: Optimization of Extractive Bioseparations in Aqueous Two-Phase Systems 7.1. Overview of Bioseparation and Process Optimizers. As shown in Figure 10, three key components of our proposed approach are the bioseparation predictor (neural network), bioseparation optimizer (response-surface model), and process optimizer (expert system). In this section, we describe how the bioseparation optimizer and process optimizer are combined to give a detailed overview of the entire extractive separation process. For protein systems with more than two components, the process optimizer determines the optimal sequence to perform the desired component splits through the use of heuristics for extractive separations. The bioseparation optimizer is used to provide an overview of the process within a given component split, showing a response-surface plot of partitioning behavior over wide ranges of operating variables (MWPEG, MWdextran,%PEG, %dextran, and pH), as shown in Figure 22. The overall architecture for the expert system shown in Figure 3 is used in our development of our separation optimizers. We use the predictions obtained from the protein-partitioning network (Figure 11)to generate a numerical database consisting of a large number of component splits that occur over wide ranges of operating conditions. This database of numerical results, In Kp,is then converted to a knowledge base of separation efficiencies, using a classification algorithm. Once the knowledge base has been generated, the heuristics set in the expert system are used to identify the optimal split sequences. There have been many heuristics previously identified for separation sequencing (Liu, 1987; Wankat, 1990). For illustrative purposes, we shall only identify the followingheuristics for the separation sequencing of this system: Carry out easy separations first and most difficult separations last. Two rules will be used for the identification of the effectiveness of a given separation:
1. The selectivity, ad,is the ratio of partition coefficients and describes the extent to which two proteins will partition to opposite phases: where selectivities of 1represent infeasible splits and as selectivity deviates from 1, the split becomes more desirable.
qj= KiIKj 2. Avoid having both components partitioning to the same phase. These two rules are classified directly from the database generated by the protein-partitioning network (Figure 11). We classify the selectivity as follows: (1) very low selectivity; (2) low selectivity; (3) medium selectivity; (4) high selectivity; (5) very high selectivity. Similarly, we classify the phase location as follows: (1)poor, both proteins predominantly in one phase; (2) medium, one or both proteins evenly split between phases; (3) good, two proteins in opposite phases. The separation efficiency is classified based on a combination of these two parameters and are categorized into the following classes: (1)infeasible; (2) poor separation efficiency; (3) fair separation efficiency; (4) good separation efficiency; ( 5 ) very good separation efficiency. Table 17 shows how the expert system assigns separation efficiencies from both the selectivity and phase classes. The classifier is designed to err toward the infeasible class. With all component splits being classified, the expert system rank-orders the separation efficiencies to determine the best sequences for the separations to be carried out. 7.2. Development of the Bioseparation and Process Optimizers and an Illustrative Application. In this section, we illustrate a step-by-step procedure for identifying the optimal separation conditions for multicomponent protein solutions. As an example, we also demonstrate the optimization of extractive bioseparations in the ATPs of PEG and dextran for partitioning four proteins, chymotrypsinogen-A (Chym), lysozyme (Lys), bovine serum albumin (Bov), and catalase (Cat). Step 1. Set protein-system and polymer-solution constraints. The input parameters for protein properties that the user needs to enter include the molecular weight and amino acid compositions. Note that if experimental data for any of the properties such as secondary structure are available, they can be used to replace the corresponding subnetwork predictions. All of the system parameters are internal to the expert network and are set based on the boundaries used in the training of neural networks. They can be changed through the definition of the search space. Input parameters. Protein system: (1) lysozyme (Lys);(2) chymotrypsinogen-A (Chym);(3) Bovine serum albumin (Bov); (4)catalase (Cat).
Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 2683
Step 2. Initialize the search space for all partitioning possibilities occurring from the protein and polymer systems defined in step 1. The magnitude of this problem is demonstrated below where we have 160 experimental systems to analyze, 640 partition coefficients to predict, and 480 component splits to consider. (i) Calculate the number of experimental systems in the search range:
A
I
no. of exptl systems = no. of MWpE, x no. of MWdextrmx no. of pH values x no. of compositions = 4 x 4 x 5 x 2 = 160 (ii)Calculate the number of potential separation splits in the search range:
-D
low
high
% Dextran Figure 23. Illustration of PEG and dextran concentration limits.
System Parameters. (i) Set molecular-weight search range. M W p E G = (4,000
no. of component splits = no. of exptl systems x [no. of proteins - 11 = 160(4 - 1)= 480
6,000 10,000 20,000)
MWdextran = ( 10,000 40,000 110,000 500,000)
Step 3. Generate protein-partitioning coefficient matrix which contains all of the system parameters a t the levels defined in step 1. For this case, we have a four-dimensional matrix which consists of the two polymer molecular weights, pH of solution, and polymer concentration levels, as shown in Table 18. Step 4. Identify all possible component splits from the protein-partitioning coefficient matrix, categorize all feasible experimental systems into component-split groups, and select the optimal separation within the group to represent that group for separation sequencing.
(ii) Set pH search range: pH = ( 5 , 6, 7, 8, 9) (iii) Set compositions of the two polymers in the aqueous solution. Use the two extreme limits for %PEG and %dextran, one a t the low concentrations near the plait point (low APEG and Adextran) and the other a t high concentrations (high APEG and Adextran). See Figure 23 for a representation of where the concentration limits are chosen. Each phase diagram will have a different composition based on its actual shape and position on the ternary diagram.
Table 18. Protein-Partitioninpcoefficient Matrix Low Polymer Concentration M w PEG at p H 4 000
Mw dextran 10000
40000
110000
500000
Lys Chym Bov Cat Lys Chym Bov Cat Lys Chym Bov Cat Lys Chym Bov Cat
6 000
20 000
10 000
5
6
7
8
9
5
6
7
8
9
5
6
7
8
9
5
6
7
8
9
1.46 1.15 0.11 0.19 1.33 1.23 0.28 0.13 1.74 1.64 0.28 0.23 1.93 1.32 0.25 0.29
1.09 1.15 0.06 0.48 1.21 1.23 0.23 0.21 1.27 1.19 0.21 0.03 1.44 1.25 0.14 0.02
0.93 1.04 0.06 0.44 1.15 1.24 0.24 0.23 1.19 0.51 0.17 0.04 1.26 0.94 0.13 0.09
0.80 0.91 0.08 0.23 1.03 1.19 0.31 0.34 1.15 0.73 0.21 0.15 1.39 0.95 0.27 0.43
0.61 0.96 0.20 0.23 0.82 1.25 0.56 0.56 0.76 2.17 0.66 0.63 0.78 0.92 0.86 0.73
1.04 1.03 0.26 0.32 1.21 1.07 0.49 0.28 1.37 1.41 0.68 0.47 1.37 2.10 0.55 0.23
0.92 1.14 0.21 0.55 1.18 0.87 0.44 0.42 1.51 1.31 0.52 0.26 2.01 1.13 0.38 0.08
0.87 1.25 0.21 0.57 1.19 0.78 0.42 0.42 1.21 1.27 0.42 0.34 1.38 0.72 0.36 0.20
0.80 1.29 0.30 0.48 1.10 0.85 0.51 0.50 0.87 1.25 0.60 0.73 0.95 0.77 0.62 0.46
0.65 1.20 0.53 0.66 0.83 0.93 0.93 0.60 1.08 1.38 1.74 0.94 0.88 1.24 0.97 0.84
1.19 1.09 0.26 0.84 1.27 0.84 0.29 0.42 1.47 1.42 0.31 0.27 1.25 1.39 0.29 0.24
0.94 1.22 0.23 0.61 1.03 0.88 0.26 0.15 1.28 1.32 0.22 0.07 1.18 0.86 0.18 0.03
0.89 1.23 0.20 0.27 1.03 0.65 0.24 0.15 1.26 1.19 0.18 0.07 1.71 0.57 0.17 0.09
0.90 0.93 0.21 0.29 1.06 0.49 0.27 0.25 0.89 0.97 0.26 0.24 0.88 0.55 0.24 0.26
0.73 1.26 0.40 0.39 0.76 0.89 0.50 0.86 0.70 1.30 0.63 0.38 0.63 0.98 0.49 0.41
1.43 0.86 0.05 0.07 1.44 1.16 0.20 0.19 1.62 1.19 0.17 0.21 1.53 1.21 0.19 0.18
0.98 0.49 0.05 0.12 1.10 0.98 0.18 0.04 1.46 1.06 0.12 0.05 1.07 1.69 0.15 0.02
0.74 0.40 0.05 0.11 1.05 0.65 0.15 0.03 1.46 0.96 0.09 0.03 0.85 1.05 0.16 0.04
0.61 0.55 0.05 0.04 1.03 0.67 0.21 0.06 1.29 0.95 0.19 0.12 0.89 0.94 0.24 0.16
0.50 1.03 0.05 0.04 0.72 1.12 0.37 0.86 0.79 1.50 0.34 0.37 0.59 1.10 0.43 0.32
8
9
5
6
High Polymer Concentration MW PEG at DH
Mw dextran
Lys 1.93 10000 Chym 1.57 Bov 0.02 0.05 Cat Lys 2.70 40 000 Chym 1.88 Bov 0.05 Cat 0.05 Lys 2.85 110000 Chym 2.49 0.08 Bov 0.05 Cat Lys 2.65 500000 Chym 1.77 Bov 0.06 Cat 0.05
20 000
10 000
6 000
4 000 5
6
7
8
9
5
6
7
8
9
5
6
7
1.37 1.02 0.01 0.03 2.00 1.15 0.04 0.01 1.96 1.82 0.06 0.01 1.56 1.33 0.03 0.01
1.08 0.72 0.01 0.01 1.74 0.92 0.04 0.01 1.76 2.01 0.05 0.01 1.25 1.80 0.02 0.02
0.76 1.20 0.02 0.01 1.24 1.80 0.05 0.01 1.39 3.15 0.05 0.03 1.67 1.56 0.05 0.07
0.45 1.52 0.04 0.04 0.61 1.98 0.09 0.37 0.80 3.51 0.10 0.17 0.74 1.38 0.20 0.20
2.00 1.57 0.05 0.04 2.93 1.84 0.09 0.05 2.69 2.26 0.14 0.09 2.13 2.75 0.06 0.09
1.29 1.00 0.04 0.02 2.04 1.42 0.07 0.01 1.78 1.67 0.11 0.01 1.18 2.47 0.03 0.01
1.01 0.65 0.04 0.01 1.75 1.30 0.06 0.01 1.46 0.99 0.09 0.01 0.88 3.19 0.02 0.03
0.86 0.99 0.05 0.01 1.43 2.20 0.07 0.01 1.32 1.67 0.09 0.04 1.02 1.89 0.03 0.07
0.58 1.45 0.13 0.10 0.68 2.16 0.10 0.36 0.74 2.56 0.15 0.14 0.51 1.24 0.15 0.18
1.70 1.03 0.05 0.10 2.61 1.82 0.09 0.06 3.09 2.25 0.10 0.06 2.46 1.64 0.06 0.04
1.01 0.49 0.04 0.10 1.58 1.73 0.08 0.02 1.92 2.02 0.08 0.01 1.32 1.47 0.04 0.01
0.67 0.32 0.04 0.05 1.12 1.16 0.07 0.01 1.33 3.48 0.06 0.01 0.81 1.79 0.03 0.01
0.53 0.45 1.86 1.36 0.63 0.84 1.08 0.76 0.04 0.04 0.04 0.06 0.05 0.19 0.03 0.03 0.95 0.69 2.05 1.40 1.32 1.35 1.31 0.74 0.06 0.07 0.07 0.09 0.01 0.19 0.03 0.03 1.01 0.76 2.25 1.42 2.91 2.22 0.72 0.91 0.05 0.07 0.05 0.04 0.01 0.03 0.04 0.02 0.90 0.44 2.36 1.21 1.48 1.40 0.98 0.83 0.04 0.09 0.08 0.06 0.03 0.03 0.03 0.01
7
8
9
0.91 0.50 0.07 0.03 0.94 0.37 0.09 0.02 0.94 1.20 0.03 0.01 0.62 0.89 0.05 0.01
0.53 0.45 0.06 0.02 0.66 0.35 0.09 0.02 0.72 2.05 0.02 0.02 0.66 1.35 0.06 0.03
0.27 1.04 0.05 0.02
0.48 1.14 0.08 0.24 0.57 1.47 0.02 0.11 0.38 1.47 0.08 0.05
2684 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 ,-
T
Chym Bov Cat
,
,
Selectivity Efficiency Classification pH = 5 . 0
Chym Bov Cat
Chym
400000
300000
a = 4.4 (fair)
a = 3 0 (fair)
2
I
/-
/
500000 1
’’
200000 100000
Fair .’
o l
I 0
5000
10000
15000
20000
25000
M w (PEG) Selectivity Efficiency Classification a=31 1 (good)
a = 1.1 (infeasible)
pH = 7.0
.
,-
a = 1. I (infeasible)
u ,
a=2.3 (poor)
I
0
5000
10000
15000
20000
25000
M w (PEG) Selectivity Efficiency Classification pH
Cat
a = 4 7 (poor)
Figure 24. Possible component splits for the four-protein case study of chymotrypsinogen-A, lysozyme, bovine serum albumin, and catalase. K > 1 partitions to top phase or PEG-rich phase and K < 1 partitions to bottom phase or dextran-rich phase.
There are seven possible component splits for the given protein mixture, as shown in Figure 24. Note that the infeasible component splits are only included for illustrative purposes. Figure 24 also shows the partition coefficients for the top and bottom phases, selectivity, and corresponding separation-efficiency class. Step 5. In this step, the process optimizer is used t o determine the optimal separation sequence of the protein mixture. As previously mentioned, the only heuristics we use here for illustrative purposes are that the easiest separations are carried out first and the difficult ones are performed last. Since there is only one component split that has a separation efficiency of “good”, it should be carried out with chymotrypsinogen-A and lysozyme being partitioned to the top phase and bovine serum albumin and catalase being partitioned to the bottom phase. This leaves only two possible component splits, one for the product of the top phase and one for the product of the bottom phase. The lysozyme and chymotrpsinogen-A from the top products have a separation efficiency in the “fair”category, while the bovine serum albumin and catalase from the bottom products have no component splits outside of the “infeasible” and “poor” classifications. Therefore, this separation will require a special separation technique such as bioaffinity partitioning, and will not progress to the bioseparation optimizer of step 6. Step 6. The bioseparation optimizer is used to find the optimal operating conditions for all the system parameters of step 1for each optimal component split identified by the process optimizer in step 5. A responsesurface plot is generated for each of these component splits with the separation-efficiencyclassification as the
3 5
e p 5
500000 400000
300000 200000 100000
I1
Poor
1
0 1 0
= 9.0
5000
10000
15000
20000
25000
M w (PEG) Figure 25. Response-surface plots generated from the bioseparation optimizer for split 1 of Figure 27. dependent variable. An infeasible classification is placed in any region where the experimental system does not yield the desired component split. The response surfaces for the two component splits identified in step 5 are shown in Figure 25 for the initial four component splits and Figure 26 for the split of the top product. The overall protein-partitioning flowsheet is shown in Figure 27 with the optimal operating conditions for each split. As seen in the responsesurface plots, it is easy to identify the best operating conditions for the two separations: low pH, low WPEG, high W d e x t r a n , and high polymer concentration for split 1 and high pH for split 2. To demonstrate the use of our bioseparation optimizer to quantitatively identify the optimal separation conditions to facilitate experimental design and process development, we investigate further the partitioning of two proteins, chymotrypsinogen-A and lysozyme, i.e., split 2 in the flowsheet of Figure 27. Figure 28 illustrates that the predicted response-surface protiles for both proteins a t the isoelectric point follow closely the experimental curves from Forciniti (1991). Thus, our protein-partitioning network of Figure 11represents a fairly accurate bioseparation predictor. Figure 28 also shows that proteins with dissimilar physical properties will have different response surfaces. Chymotrypsinogen-A has a linear response profile with respect to polymer molecular weights, while lysozyme has a hyperbolic response profile. A plot of the selectivity, or
Ind. Eng. Chem. Res., Vol. 33,No. 11, 1994 2686 Partition Coefkients (In KS ) Chymotrypsinogen - A pH = 9.5 (isoelectric point)
Selectivity Efficiency Classification pH = 5 . 0
-
500000
50oooO
Poor/Infeasible
Q
p
200000 .'
300000
100000
8
o l
E
0
5000
10000
15000
ZOO00
200000
25000
100000
M w (PEG)
0
Selectivity Efficiency Classification
0
5000
20000
25000
T
Partition Coefticients (In 5 )
400000 ..
e
15000
M w (PEG)
pH = 7 . 0
, . 500000
10000
LysoYme
Poor
300000 ..
pH= 11.0 (isoclectricpoint) 50oooO 4oo000
0 1 0
5000
15000
I0000
20000
25000
M w (PEG)
p
Selectivity Efficiency Classification
pH 500000
T
400000
.'
=
10ooo0
9.0
0 0
5MO
loo00
15000
Zoo00
25000
M w (PEG)
Fair 200000
0 1 0
2OOOOO
5000
10000
15000
20000
25000
M w (PEG) Figure 26. Response-surface plots generated from the bioseparation optimizer for split 2 of Figure 27.
high p H
Lys low Mw(PEG) high Mw (Dextran) {requires special separation technique} Cat Figure 27. Overall protein-partitioning flowsheet.
the ratio of partition coefficients in the two proteins, quantifies how sharp the split will be between two proteins in a given ATPs. Figure 29 gives a plot of selectivity values for a mixture of chymotrypsinogen-A and lysozyme in ATPs at its optimal operating conditions determined by the expert system, namely, high pH. This response-surface plot will give a more quantitative representation of the process than the previous fuzzy characterization in Figure 26. As seen in Figure 29, our strategy easily identifies the optimum ranges of PEG and dextran molecular weights within the highpH response-surface plot, for maximizing the selectivity values. 8. Conclusions 1. The use of the hierarchically-structured, proteinpartitioning network of Figure 11 is very effective in
Figure 28. Experimental and predicted response-surface profiles of constant partition coefficients for protein partitioning in ATPs of PEG and dextran of various molecular weights at the isoelectric point. Solid curves represent experimental values by Forciniti (19911,and dashed curves are predicted values by the proteinpartitioning network.
developing a flexible approach to the predictive modeling and optimal design of extractive bioseparations in ATPs. 2. The incorporation of the expanded set of protein properties into our protein-partitioning network (Figure 11) has minimal effects for predicting the partition coefficient, In K,,when the pH is near the isoelectric point. However, the use of the protein-property subnetwork significantly improves the prediction capabilities of the protein-partitioning network as the pH of solution deviates from the isoelectric point, that is, for predicting the partitioning coefficient, In 3. The compartmentalized structure of the proteinpartitioning network allows for the addition of other contributing factors such as temperature, bioaffnity partitioning, and electrophoresis-induced partitioning without having to reconstruct the entire model. 4. The response-surface optimizer and process optimizer provide a user-friendly representation of the protein-partitioningcharacteristics (e.g., partition coefficient and selectivity) for a given protein mixture. Therefore, optimal operating regions can be identified with minimal experimentation.
Acknowledgment This work was supported by the Eastman Chemical Company through a fellowship grant to D.R.B., and by Neuralware, Inc., Pittsburgh, PA, through free use of their software, Neuralware Profession IWLUS. Nomenclature d = mean diameter of the ions f c l j ) = transfer function for the processing element
2686 Ind. Eng. Chem. Res., Vol. 33, No. 11, 1994 Selectivity (Ratio of Partition Coefficients) Chymotrypsinogen - A /Lysozyme
(a)
Selectivity (Ratio of Partition Coefficients) Chymotrypsinogen - A /Lysozyme
(C)
pH = 8.5
pH = 4.6 0.55 8
' E
8 0.62
8 0.50
8 0.51
1.79 8
8
1.60
1
175
8 1.98
1.81
1.72 1.98
300000 200000
.-
100000
-r
0 0
0.57 8
8 0.66
0.63 I 0.63
0.71 0.79
8 0.53
0.55
0.48
I .oo
0.56
1oooo
5wo
0.60
l5W
ZOO00
2.26
0
0
25m
2.06
5wo
2.15
1.70 25000
20000
Mw (PEG)
Selectivity (Ratio of Partition Coefficients) Chymotrypsinogen- A /Lysozyme
Selectivity (Ratio of Partition Coefficients) Chymotrypsinogen - A / Lysozyme
pH = 9.2
pH = 5.6 50oooO
500000
3.76 8
8 0.84
8 0.80
2
15000
lw00
Mw (PEG)
'E
2.17
400000
400000
8 3.78
8
8 3.56
8 3.22
3.14
8
3 80
4wooO
4 o m 300000 200000
0.59 8
8 0.81
0.63 I 0.59
0
0
5Mx)
3.13 8
8 0.93
,
low00
0.91 0.83
1ooooo
0.88 1.03
loo00
ISDO0
0.98 1.03 zoo00
25wo
Mw (PEG)
8 3.97
OpddOpdngCondltbN
I 3.90
1.64
0 0
5000
10m
15000
zoo00
25000
Mw (PEG)
Figure 29. Response-surface plots of selectivity values for partitioning of protein mixtures in ATPs of PEG and dextran of various molecular weights a t increasing pH values. Note the region of optimal operating conditions with highest selectivity values in (d).
IJ = weighted sum of input variables to a processing element minus t h e internal threshold Kb = partition contribution from affinity binding K, = partition contribution from electrophoresis Kp = overall partition coefficient KPH= partition contribution due to pH variation from t h e isoelectric point K, = partition coefficient of the polymer solution a t standard conditions (temperature a t 25 "C and pH a t the isoelectric point) Kt = partition contribution due to t h e temperature variation from 25 "C M , = number-average molecular weight M , = weight-average molecular weight PI = polydispersity index, t h e ratio of M, to M , TI= internal threshold value for processing element j w,,= weighting factor from t h e i t h input variable to t h e j t h output variable x L = input variable to a processing element yJ = output variable from a processing element a, = selectivity; ratio of partition coefficients KJK, p, = ion-ion specific interaction coefficient 612 = solubility-parameter difference between PEG and dextran dl, = solubility-parameter difference between PEG and water dzS= solubility-parameter difference between dextran and water
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824-834. Received for review November 15, 1993 Revised manuscript received June 7, 1994 Accepted June 27, 1994@ @
Abstract published in Advance ACS Abstracts, September
1, 1994.
