One of the hardest tasks in the development of our models was to come up with good strategy to generate input parameters from the raw data. In our case, the raw data is the binding site sequence and the corresponding sh/miRNA-sequence. The final parameterization concept unites a basic distinction between perfect, bulged (near-perfect) and endogenous miRNA like BS, with the advanced 3'-scoring and AU-content evaluation. The endogenous miRNA like BS parameter is further split into the three types of seed binding sites.
Neural Network Model
Neural Network theory
Artificial Neural Network usually called (NN), is a computational model that is inspired by the biological nervous system. The network is composed of simple elements called artificial neurons that are interconnected and operate in parallel. In most cases the NN is an adaptive system that can change its structure depending on the internal or(and?) external information that flows into the network during the learning process. The NN can be trained to perform a particular function by adjusting the values of the connection, called weights, between the artificial neurons. Neural Networks have been employed to perform complex functions in various fields, including pattern recognition, identification, classification, speech, vision, and control systems.
During the learning process, difference between the desired output (target) and the network output is minimised. This difference is usually called cost; the cost function is the measure of how far is the network output from the desired value. A common cost function is the mean-squared error and there are several algorithms that can be used to minimise this function. The following figure displays such a loop.
Figure 2: Training of a Neural Network.
Model description
Input/target pairs
The NN model has been created with the MATLAB NN-toolbox. The input/target pairs used to train the network comprise experimental and literature data (Bartel et al. 2007). The experimental data were obtained by measuring via luciferase assay the strength of knockdown due to the interaction between the shRNA and the binding site situated on the 3’UTR of luciferase gene. Nearly 30 different rational designed binding sites were tested and the respective knockdown strength calculated with the following formula->(formula anyone???).
Each input was represented by a four elements vector. Each element corresponded to a score value related to a specific feature of the binding site. The four features used to describe the binding site were: seed type, the 3’pairing contribution the AU-content and the number of binding site. The input/target pair represented the relationship between a particular binding site and the related percentage of knockdown.
The NN was trained with a pool of 46 data. Afterwards it was used to predict percentages of knockdown given certain inputs. The predictions were then validated experimentally.
Characteristic of the Network
The neural network comprised two layers (multilayer feedforward Network). The first layer is connected with the input network and it comprised 15 artificial neurons. The second layer is connected to the first one and it produced the output. For the first and the second layer a sigmoid activation function and a linear activation function were used respectively. The algorithm used for minimizing the cost function (sum squared error) was Bayesian regularization. This Bayesian regularization takes place within the Levenberg-Marquardt algorithm. The algorithm updates the weight and bias values according to Levenberg-Marquardt optimization and overcomes the problem in interpolating noisy data, (MacKay 1992) by applying a Bayesian framework to the NN learning problem.
Figure 3: schematic illustration of the network components. Hidden represent the first layer and it comprised 15 artificial neurons, while output is the second and last layer producing the output. The symbol “w” was the representation of the weights and “b” of the biases.
Results
Training the Neural Network
The Network was trained with 46 samples. The regression line showing the correlation between the NN outputs and the targets was R=0.9864.
Figure 4: Regression line showing the correlation between the NN output and the respective target value.
Why using a fuzzy inference system to model binding site efficiency?
To be able to evaluate the complex features of an shRNA or miRNA binding site and predict a resulting knockdown percentage of the protein we developed a fuzzy inference system (fis). The parameterized properties of the binding sites serve as input and will be processed into the knockdown percentage as the single output. Thus our fuzzy inference system is characterized as a multiple input, single output fuzzy inference system (MISO).
Fuzzy Logic is a rule-based approximate artificial reasoning method developed by Lotfi Zadeh in 1965. Its motivation is the observation that humans often think and communicate in a vague way, and yet can make precise decisions [Nelles O. Nonlinear System Identification Springer Verlag GmbH & Co., Berlin, 2000.]. It has been widely used in engineering and Artificial Intelligence approaches such as Fuzzy Controllers and Fuzzy Expert Systems. Fuzzy Logic has also been used for the modeling of biological pathways [Bosl W. J. Systems biology by the rules: hybrid intelligent systems for pathway modeling and discovery. BMC Systems Biology1:13 (2007).] and to analyze gene regulatory networks [Laschov D., Margaliot M. Mathematical modeling of the lambda switch:a fuzzy logic approach. J Theor Biol. 21:475-89 (2009)]. Key advantages of Fuzzy logic-based approaches are (i) the ability to construct models based on prior knowledge of the system and experimental data and (ii) encode intermediate states for inputs and outputs, thus improving other logic-approaches that can only deal with ON/OFF states such as Boolean models [Aldridge B. B., Saez-Rodriguez J., Muhlich J. L., Sorger P. K., Lauffenburger D. A. Fuzzy logic analysis of kinase pathway crosstalk in TNF/EGF/insulin-induced signaling PLoS Comput Biol.5:e1000340 (2009).] and (iii) simulations can be derived from both qualitative and quantitative data, both of which can be cast into the form of IF-THEN rules. Thus, FL constitutes a powerful approach for the understanding of heterogeneous datasets.
Fuzzy inference systems are based on membership functions (MF). MF rate input parameters on a scale from 0 to 1, how much they satisfy a criterion. There can be one, or multiple criteria – called membership function - for one input parameter. The height of persons for example can be evaluated with one MF - how much the person satisfies being tall. On the other hand, there could be 3 MFs, one evaluating the membership to small people, the second to medium sized people and the third one to big people (Figure MembershipFunction1.png). In case of a persons height of 1.8 meter the MF “big” would be satisfied to about 0.6 (Figure MembershipFunctionBig.png). Like this, all input is converted to membership values from 0 to 1. Changing the shape of the MF gives the opportunity to have either functional dependencies, allowing intermediate states of the membership values, or simple ON/OFF states, where the membership value can be only 0 or 1 (Figure MembershipONOFF.png). Thus different kinds of input parameters can be evaluated with a fuzzy inference system. For the simple height example model the age of the person could be taken as second input and evaluated by a MF that is 0 until the age of 18 and 1 for older persons. Thus the model would differentiate between young and grown-up persons.
Simple if-then rules can then be used to combine the input MF to an output MF. The satisfaction of a rule by an object (set of input parameters) is defined by the degree of membership of the object to the different MF. The higher the satisfaction of the rule, the higher is the membership to the output MF.
The output MF can be a function like the input MF. This is the case in Mamdani method fuzzy inference systems [Mamdani, E.H. and S. Assilian, "An experiment in linguistic synthesis with a fuzzy logic controller," International Journal of Man-Machine Studies, Vol. 7, No. 1, pp. 1-13, 1975.]. We are using a Sugeno method fuzzy inference system [Sugeno, M., Industrial applications of fuzzy control, Elsevier Science Pub. Co., 1985.], where the output MF is either a constant or a linear function depending on input parameters. The advantage of a Sugeno fuzzy inference system is, that it is computationally more efficient and easier to optimize or adapt due to the more simple output MF. Due to the non-intuitive combination of the 3'-pairing and AU-content score, our fuzzy inference system needs to be optimized computationally.
How is our fuzzy inference system optimized?
MISO Sugeno Fuzzy Network Model
Optimizable
Extendable
Fuzzy Model Concepts
Bulged binding sites concept: This model concept evaluates bulged- or "near-perfect" binding sites separately from conventional seed + 3'-pairing binding sites. Rule number 2 considers the bulge-size of the bulged binding site.
Bulged binding sites (including AU-content-score) concept: This concept extends the bulged-BS concept with the addition of AU-content score evaluation. Therefore rule number 2 was modified accordingly.
Consider low 3' score concept: This model concept takes into consideration, that binding sites with a 3'-score under 3 did not show a significant change in knockdown efficiency compared to a control with only seed pairing (Grimson et al., 2007). This is realized by rule number 6.
Strength: general prediction, no dependency on conditions. Assured by [normalization strategy]
based on previous knowledge [Bartel]
Our fuzzy inference system can deal with 3 different kinds of shRNA binding sites. Perfect, bulged and endogenous-like binding sites are treated separately, due to the differences in their biological mechanism, as discussed earlier [link to binding site properties].
A perfect binding site is evaluated by a simple ON/OFF input MF evaluating the boolean input of
We came up with different concepts of what kind of input parameters to integrate into the fuzzy inference model and how to evaluate them. Therefore we parameterized the properties of a large set of binding sites according to various different BS characteristics.
The targetscan_50_context_scores – Algorithm (Rodriguez et al., 2007) which evaluates binding sites in respect to 3'-pairing and AU-content gives out a score that seems appropriate to distinguish especially between endogenous miRNA like binding sites. A more detailed description on the concept of binding site parameterization can be found under Model Training Set.
"
