a)

b)

Neural Networks in Transcription Networks: An alternative and complementary approach for the observer-based method

Jorge Guerra Pires Faculty of Applied Physics and Mathematics/ Faculty of Engineering

Gdansk University of Technology (GUT)/ University of L’Aquila (UAQ) Gdansk, Poland/L’Aquila, Italy

jorge.guerrapires@mathmods.eu/ jorgeguerrapires@yahoo.com.br

Abstract— on the current manuscript, we dissert on the application of Artificial Neural Network (ANN) as alternative and complementary approach for the observer-based method in transcription network; which is a recent proposed tool for modeling transcription networks. In view of that, it is claimed that neural networks as models for applied mathematics may solve the problem of gene expression estimation addressed by the technique with some advantages inherent in the technique compared to the observer-based method; the target is enforcement, not denying. Thus, systems biology is the gene-based science under attention and computational intelligence is the intelligence-based tool under investigation.

Keywords— Artificial Neural Networks; Transcription Networks; Observer-based method; Systems Biology;

I. INTRODUCTION

In this work, it is defended the application of Artificial Neural Network1 (ANN) in Transcription Networks as alternative and complementary approach for the observer-based method applied in gene expression estimation. Accordingly, it is meant ‘complementary’ in the implication that they may work together for “solving”2 a real biological problem and ‘alternative’ in the implication that it is proclaimed that neural networks may be applied to solve the problem per se, without knowledge of the observer-based method; besides the observer-based method may support the modeling. Ideally, in general, methods such as neural networks are strongly dependent on initial states before it starts to work and if the initial state is not properly provided, it might even diverge (not generalizing.) One may see here an application of neural networks for supporting an analytical model for a biological problem of quite complex nature and at the same time a modeling procedure for a non-linear physical problem.

Consider the scheme just presented, fig. 1. This shows two sides of the theory for modeling systems. The first scheme (a) presents the modeling of physical systems as a cyclic action of modeling and improving (Measurement-Analysis dichotomy); the second scheme (b) shows as a set of variables under control and some noisy, one is endowed with an input signal that triggers some dormant behaviors. This input signal is employed to give rise to responses in the workings of the system. The second scheme in the presented picture (fig. 1.b) depicts the

1 Shortly referred as neural networks. 2 Hereafter accept “solve” as approximation. This problem is not simple, as may be found in books and papers; most of the theory are models under assumptions.

most important and useful view of mathematical modeling: for one learns about a system, it is necessary to “excite” it.

Figure 1. Physical System Modeling.

Accordingly, one might point out two possibilities when one applies mathematical models to physical systems: a) Blind Models (BM); b) Partial Blind Models (PBM). By BM it is meant models without references to shapes, such as functions. One example is non-parametric regressions and a second example is neural networks; other models are possible. By PBM it is meant models that partially guess the mathematical-shape of the ‘black box,’ such as the State Observer in System Control Theory (SCT) [3], linear regression [4], or some application of neural networks; other cases are possible.

A. Problem description As it may be found claimed in [1], due to technological

limitations, this is not possible to measure directly the protein concentration as a consequence of cellular physical interferences and others. However, it is possible to measure the mRNA concentration, which represents the promoter activityof the corresponding gene.

Thus, “Though we would like to measure the protein abundance directly, it turns out to be much easier to measure the relative mRNA levels in cell, and so in practice that is often done. It is important to keep in mind, however, that this is only an indirect measure of the protein levels, since there are many other factors which determine how much and how fast the mRNA gets translated into protein” ([2], p.430). The bridge ‘mRNA-protein’ is in general done via mathematical models; in some case via simple interpolations, as claims some researchers in the area.

1st BRICS Countries Congress on Computational Intelligence

978-1-4799-3194-1/13 $31.00 © 2013 IEEE

DOI 10.1109/BRICS-CCI.&.CBIC.2013.49

282

1st BRICS Countries Congress on Computational Intelligence

978-1-4799-3194-1/13 $31.00 © 2013 IEEE

DOI 10.1109/BRICS-CCI.&.CBIC.2013.49

282

2013 BRICS Congress on Computational Intelligence & 11th Brazilian Congress on Computational Intelligence

978-1-4799-3194-1/13 $31.00 © 2013 IEEE

DOI 10.1109/BRICS-CCI-CBIC.2013.53

282

Hence, as proposed by [1], it is interesting and feasible to use a mathematical model to predict the protein concentration; more precisely, a ‘mathematical-observer.’ The mathematical model is called the observer-based method, or State Observer; some prefers to call it ‘approximator,’ once it does not actually ‘observers’ the physical system. Thus, it tries to predict “hidden” variable via “well-known” ones. On the other hand, it is well-known from practical problems that neural networks have the ability to extract “hidden laws” and then making them available for posterior use. Having it in mind, the problem comprises: a) ‘estimation of gene expression (GEE)’; b) ‘the solution presented via the observer-based method’; and c) ‘the neural network theory as mathematical modelling tool’. Further, it is chased the question: “How may I apply neural networks to predict the gene expression based on other measurable parameters, such as the mRNA concentration and some bio-parameters?” This is done keeping in mind how to take advantage of the work developed by [1] and group.

II. THE STATE-OBSERVER METHOD

As defends [1], it is not possible to measure directly the gene promoter activity, it is done by means of mRNA concentration measurement instead of the direct inference of the protein concentration produced by the gene. It means that instead of measuring the protein concentration directly as it supposes to be done, it is measured the mRNA concentration responsible for encoding the protein under question. In the paper [1], a mathematical tool (the observer-based method) is presented to estimate unknown variables of transcription networks. The mathematical tool presented is according to a set of indirect measurements of the promoter activity. The state observer allows tracking the time course of the “hidden variables” of the system by measuring the “visible” variables. Furthermore, the observer-based approach is an interesting mathematical tool for state estimation problems when a dynamical model3 of the system under study is available and it may be seen as complementary to other statistical approaches [1].

III. OBSERVER-BASED METHOD VS ARTIFICIAL NEURAL NETWORKS (ANN)

Following, it was built a table to compare the two mathematical tools; see table I.

IV. FINAL CONSIDERATIONS

In principle, two neural networks sound quite promising for the application in consideration: Static Feedforward Networks or Dynamical Feedforward Networks. The former is justifiable due to the simplicity compared to other networks and also due to the extensive use, it has proved to be quite efficient; the latter is justifiable due to the recurrent feature, feedbacks. Recurrent networks are known for being successful networks that exhibit the peculiar attribute of allowing the signal going backward; it might be useful, since we have auto-regulations [5] in transcription networks.

3 This might be a drawback. Besides it is known toy models based on networks and dynamical systems theory, the real law behind the model might be a little more complex, even the dynamical systems giving nice and “handsome” equations.

In feedforward-networks, the signal just travels forward, never backward. Feedforward neural networks are stable, where recurrent networks might be or not since they are dynamical systems; the proof of stability might evolve lyapunov functions, which is not simple at all. Likewise, when one ‘trains’ an observer, this is indirectly a learning procedure; using the concept of eigenvalues and poles, it is chased to minimize an error function by choosing properly the eigenvalues (negative) of a matrix; this matrix is generated from the parameters of the systems and a ‘gain’-vector.

TABLE I. STATE OBSERVER APPROACH COMPARED TO NEURAL NETWORK

Approach Observer-based method Neural networks

Interesting when one has the dynamical model of the system under question.

Do not require assumptions of the ‘shape’ of the system.

Observers are designed for deterministic systems, but biological data are in general noisy.

One of the best points about neural networks is the tolerance to noise, “mistakes.”

It is considered continuous-time systems of differenrial equations, but real measurements are discrete.

Neural networks have to be trained in a discrete manner, otherwise the training will not be effective.

ACKNOWLEDGMENT

J.G.P would like to thank the Gdansk University of Technology for granting him the title of master of science, in special prof. Rybicki. As well, the author is in debt with prof. P. Palumbo (Institute of Systems Analysis and Computer Science, IASI-CNR) for all the discussions in the observer applied to transcription networks. Additionally, the author is in debt with prof. Rubino (Università Degli Studi Dell'Aquila) as well the Università Degli Studi Dell'Aquila for granting him the second title of master (Laurea Magistrale). For the sponsorship, JGP thanks Maury de Souza Jr. (Private Funds) and ADSU L'Aquila (Azienda per il Diritto Agli Studi Universitari dell'Aquila) grant (2011/July).

REFERENCES

[1] F. Cacace, A. Germani, P. Palumbo, ‘The state observer as a tool for the estimation of gene expression’, Journal of Mathematical Analysis and Applications, Vol.391, pp.382-396. 2012.

[2] W. J. Ewens, G. R. Grant, Statistical methods in bioinformatics: an introduction, Second Edition, Spring, 2005.

[3] R. C. Dorf, R. H. Bishop, Modern control systems, Eleventh Edition. Prentice Hall, 2008.

[4] G. C. Runger, D. C. Montgomery, Applied Statistics and Probability for Engineers, 3rd edition, [e-Text CD-ROM], John Wiley & Sons, Inc, 2003.

[5] U. Alon, An Introduction to systems biology: design principles of biological circuits, Chapman & Hall/CRC, 2006.

283283283