MLP Neural Network Modeling of PEG – Dextran, Polymer – Polymer Aqueous Two-Phase Systems

July 15, 2017 | Autor: Javad Hekayati | Categoria: Artificial Neural Networks, Aqueous Two-Phase Systems
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th

The 15 Iranian National Congress of Chemical Engineering (IChEC 2015)

University of Tehran, Tehran, Iran, 17-19 Feb. 2015

MLP Neural Network Modeling of PEG – Dextran, Polymer – Polymer Aqueous Two-Phase Systems Aliakbar Roosta* Javad Hekayati Jafar Javanmardi Chemical Engineering, Oil and Gas Department, Shiraz University of Technology, Shiraz, Iran *[email protected]

Abstract Aqueous two-phase systems (ATPSs) are formed because of the mutual incompatibility of two hydrophilic polymers or a polymer and a salt which are increasingly being applied in extractive separation and purification of macromolecules, particles and biological materials which are fragile and susceptible to denaturation if undergone classical separation processes. This advantageous feature could mainly be attributed to the low surface tension between the two liquid phases and also the generally benign environment of the system. The deployment of ATPSs is especially promising in overcoming low product yield in conventional fermentation processes. In this study an artificial intelligence model based on a feedforward back-propagation neural network was employed to predict the partition coefficients of the two polymers comprising ATPSs of PEG – Dextran of varying molecular weights as one of the most common aqueous two-phase system currently employed. These partition coefficients are essential in proper engineering of extractive separation of biomolecules. The results indicate the applicability of the neural network model as a reliable technique for the optimization of extraction conditions. Keywords: Aqueous Two Phase System, PEG, Dextran, Artificial Neural Network, Partition Coefficient

Research Highlights •

• •

MLP Neural Network modeling of ATPSs of PEG – Dextran of a variety of molecular weights. Accurate prediction of the partition coefficients of the polymers constituting the system. AARD/% deviations of less than 0.13.

MLP Neural Network Modeling of PEG – Dextran

1. Introduction Product inhibition, i.e. the harmful effect of the presence of products on the enzyme reaction with substrate which results in low product yield in conventional fermentation processes has been successfully dealt with by employing ATPSs. Furthermore, the purification and separation of products in the field of biochemical engineering is considered to determine 5090% of the final product cost; aqueous two-phase systems with their relatively low cost and especially excellent partitioning capabilities are promising in this regard. In addition, the possibility of retaining the reactants in the bottom phase, secluded from overhead air, makes ATPSs ideal as a simple set-up for anaerobic reactions. Furthermore, Artificial Neural Networks are computational models designed to incorporate key features of, and process data in a manner analogous to neurons in animal's central nervous systems (in particular the brain) which are capable of machine learning as well as pattern recognition. In this work, an attempt is made to examine the applicability of a multilayer feedforward neural network with backpropagation training in predicting the partition coefficients of the two polymers comprising ATPSs of PEG – Dextran of varying molecular weights. 2. Methods Since their discovery in 1896, a wide variety of polymer-polymer or polymer-salt mixtures have, and are still being proposed on a regular basis; Nonetheless, PEG-Dextran ATPSs of various molecular weights remain to be one of the most popular polymer-polymer combinations to date. In this work, the required experimental LLE datasets of the systems of interest were retrieved from the handbook of Boris Y. Zaslavsky (1994) [1]. A summary of the temperature, molar mass (‫ܯ‬௪ ) as well as the number average molar mass (‫ܯ‬௡ ) of the polymers of each ATPS, alongside the number of data points of each set are reported in Table (1). Table 1. Temperature & Molecular Weight of the Polymers Constituting the Database T (K) ‫ܯ‬௪ PEG ‫ܯ‬௡ PEG ‫ܯ‬௪ DEX ‫ܯ‬௡ Dex Total No. 295.15 3400 3400 40200 24400 20 277.15 3400 3400 388000 24200 20 295.15; 277.15 3400 3400 72200 38400 40 295.15; 277.15 3400 3400 507000 234200 40 298.15 4100 3800 19300 13200 20 277.15; 313.15 4100 3800 19300 13200 40 298.15; 277.15; 313.15 4100 3800 37000 27700 60 298.15; 277.15; 313.15 4100 3800 86200 52100 60 298.15; 277.15; 313.15 4100 3800 215000 88200 60 298.15; 277.15; 313.15 5600 5300 19300 13200 60 298.15; 277.15; 313.15 5600 5300 37000 27700 60 296.15; 281.15; 311.15; 323.15 6000 6000 57200 28700 115 595

2.1. Artificial Neural Network

The procedure with which the ANN, fed with input variables, reaches at target variables, has been described adequately by Bishop and Roach [2], so no attempt is made here to reproduce

th

The 15 Iranian National Congress of Chemical Engineering (IChEC 2015)

University of Tehran, Tehran, Iran, 17-19 Feb. 2015

the details. In short, neural networks are made up of an arbitrary number of layers, each consisting of several neurons. A parameter known as weight (ܹ௜௝ ) is associated with each connection between two neurons. Practically, each neuron in hidden or output layer firstly acts as a summing junction, which combines and modifies the inputs from the previous layer. The output of each neuron is determined by application of a suitable transfer, usually sigmoid, function to this weighted sum. Next, a back-propagation learning algorithm is employed to update the weights and biases in the direction in which a suitably chosen performance function decreases most rapidly. Using The Levenberg-Marquardt algorithm [3-4] as the back-propagation learning algorithm of choice, the optimized topology of the ANN, i.e. the number of hidden layers themselves alongside the number of hidden layer(s) neurons are determined. 3. Results and Discussion After many attempts, the best network obtained is a one-hidden layer MLP with 10 neurons in the hidden layer, which corresponds to the least AARD% and MSE as defined in equation (1). The transfer functions best suited to this investigation were determined to be Hyperbolic Tangent Sigmoid for the hidden and Symmetric Saturating Linear Transfer Function (Satlins) for the output layer. The parameters of the proposed ANN structure, as illustrated in Figure (1), are shown in Table (1). In addition, the AARD/% and MSE values for training, validation and test data are listed in Table (3).

1 1 N kexp − kcalc AARD/% = ∑ , MSE = N N i =1 kexp

N

(kexp − kcalc )2 ∑ i =1

(1)

Note that the data were split randomly to allocate 70% as the training and the remaining used as the network validation and testing data, both in equal measure.

Figure 1. Schematic diagram of the proposed ANN model

MLP Neural Network Modeling of PEG – Dextran

Table 2. Parameters of Hidden and Output Layers of the Proposed ANN

Hidden Layer Weight Matrix 3.723 -0.089 0.277 2.622 -0.52 0.25 9.797 -3.543 -1.722 -1.686

3.256 -0.115 0.262 2.198 -0.367 0.283 9.732 -3.322 -1.132 -1.365

-0.314 -1.026 -0.1 -0.576 3.013 0.234 -14.843 9.153 1.199 0.589

-1.593 0.926 -0.447 1.767 -2.862 -0.005 -19.651 15.413 -0.275 -1.245

-0.819 0.295 4.444 1.184 -3.102 -3.961 -14.618 14.459 0.633 0.097

Bias Vector

Output Layer Transposed Bias Weight Matrix

-2.077 -1.321 4.033 2.033 -0.387 -3.554 -11.789 -0.135 -1.357 -2.912

-0.491 2.234 2.338 0.406 0.493 2.031 -0.102 0.419 0.345 -1.308

0.327 -0.349 -1.958 -0.422 0.088 -1.174 0.08 -0.103 -0.519 2.178

0.39

1.581

Table 3. Overall AARD/% and MSE Values for Training, Validation and Test Data of the Proposed ANN

Training Data AARD/% MSE 0.134 0.033

Validation Data AARD/% MSE 0.119 0.022

Test Data AARD/% MSE 0.098 0.017

Also keep in mind that in order to sensitize the ANN to the fact that several different feed compositions on any given tie-line would result in exactly the same final compositions in top and bottom liquid phases and hence the same partition coefficients, the dataset reported in Table (1) incorporates 5 data points on each experimental tie-line. In addition, and since the partition coefficients of PEG and Dextran in the two liquid phases usually differ by several orders of magnitude, the target variables of the ANN were opted to be in the logarithmic scale, as seen in Figure (1).

0.5

90

0.45

80

0.4

70 ANN KDextran

ANN K PEG

0.35 60 50 40 30

0.3 0.25 0.2 0.15

20

0.1

10

0.05 20 40 60 80 Experimental KPEG

0.1 0.2 0.3 0.4 0.5 Experimental K Dextran

Figure 2. Experimental vs. Predicted Values

th

The 15 Iranian National Congress of Chemical Engineering (IChEC 2015)

University of Tehran, Tehran, Iran, 17-19 Feb. 2015

4. Conclusions As a simple, computationally non-intensive and yet accurate artificial intelligence model of the partition coefficients of the polymers constituting the ATPSs of PEG-Dextran, an MLP network was constructed based on experimental liquid-liquid equilibrium data. The results demonstrate the acceptable precision with which the proposed ANN is capable to correlate the system feed composition, alongside temperature and number average molecular weight of its constituents to the desired partition coefficients. References [1]

Zaslavsky, B. Y., Aqueous Two-Phase Partitioning: Physical Chemistry and Bioanalytical Applications, vol. 15. CRC Press, p. 656., 1994

[2]

Bishop, C. M., Roach, C. M., “Fast curve fitting using neural networks,” Rev. Sci. Instrum., vol. 63, no. 10, p. 4450, 1992.

[3]

Hagan, M. T., Menhaj, M. B., “Training feedforward networks with the Marquardt algorithm.,” IEEE Trans. Neural Netw., vol. 5, no. 6, pp. 989–993, Jan. 1994.

[4]

Levenberg, K., “A method for the solution of certain non-linear problems in least squares,” Q. J. Appl. Mathmatics, vol. 2, pp. 164–168, 1944.

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