Combinatorial Multi-Component Therapies of Drugs using Pruned GMDH Algorithm

Tejinder M Aggrwal1, Abhijit Pandya1 and Larry Liebovitch2
1Florida Atlantic University, Department of Computer Science and Engineering, Boca Raton, FL 33431
2Florida Atlantic University, Center for Complex Systems and Brain Sciences, Center for Molecular Biology and Biotechnology, Department of Psychology, Department of Biomedical Science, Boca Raton, FL 33431

ABSTRACT
Multi-component therapies, originating through deliberate mixing of drugs in a clinical setting, through happenstance, and through rational design, have a successful history in a number of areas of medicine, including cancer, infectious diseases, and CNS disorders. Use of single drug for complex biological processes, where in fact redundancy and multi-functionality are the norm, fundamentally limits the therapeutic index that can be achieved by a most potent and highly selective drug. Thus, it will almost certainly be necessary to use even new “targeted” pharmaceuticals in combinations. Drugs designed for a specific target are always found to have multiple effects. Rather to hope that one bullet can be designed to hit only one target, nonlinear interactions across genomic and proteomic networks could be used to design Combinatorial Multi-Component Therapies (CMCT) that are more targeted with fewer side effects.
This paper reviews the opportunities and challenges inherent in the application of non-linear interactions of neural networking using pruned GMDH Algorithm with specific reference to the possibility of achieving combinatorial selectivity with multi-component drugs. Using a nonlinear model of how the output effect depends on multiple input drugs, an artificial neural network can accurately predict the effect of all 215 = 32,768 combinations of drug inputs using only the limited data of the output effect of the drugs presented one-at-a-time and pairs-at-a-time. Systematic combination screening may ultimately be useful for exploring the connectivity of biological pathways. When performed this approach may result in the discovery of new combination drug regimens having least side effects targeting multiple actions.
Combination or multi-component therapy, in which one or more drugs are used at the same time, was first explored at a theoretical level (Loewe, 1928) and typically has several goals, such as: reducing the frequency at which acquired resistance arises by combining drugs with minimal cross-resistance; lowering the doses of drugs with non-overlapping toxicity and similar therapeutic effects so as to achieve efficacy with fewer side effects; using one or more chemotherapeutic drugs to sensitize cells to the action of additional drugs; exploiting additivity, or better-yet, synergism, in the biochemical activities of two drugs so as to achieve significantly greater potency than is possible with either drug on its own.
. Neural networks are generally considered "black boxes" of memory (Pandya and Macy, 1995). In other words a researcher may know the precise values of inputs, the precise values of outputs and the precise values of the connections weights without any knowledge of precise mathematical expressions for the relationships, because, such modeling is quite difficult with complex networks. Most of the programs available for neural networks do not design the network by assigning weights but they train the networks to give desired output for given input, and then record the weights.
The algorithm developed in this paper provides a solution to the above problem. Each neuron in the hidden layer can be represented using a quadratic polynomial equation involving any two neurons from the previous layer. This gives insight into the network and clearly defines the relationship between the neurons in a layer and the neurons in a previous layer making it easier to understand even for complex networks. Such visualization shows the dynamics of learning allow for comparison of different networks and show differences due to regularization and optimization procedures.
GMDH (Ivakhnenko, 1971) algorithm forms a basis for the algorithm proposed in this work. However several modifications are made to the basic GMDH algorithm to meet all the goals of the proposed algorithm and provide a pruned network. The new algorithm follows a similar method as that used in regression analysis in order to calculate the weights for the neuron functions. Though not originally designed for the purpose of calculating weights in a neural network, it can be easily adapted for this modern purpose. The proposed algorithm combines the best procedures from the variations on the GMDH method (Kondo & Pandya, 2000) in order to quickly produce the smallest, most accurate network possible.
This algorithm is then applied to analyze Drug Test Data (Liebovitch et al, 2006). The development of a new drug is a complex and expensive process. Current estimates place the total development costs of a new drug (including the writing off of false starts, clinical trials and tests required by regulatory authorities) somewhere in the region of 800 million dollars. As using combination of drugs to determine which combination can provide a better therapeutic effect is an expensive procedure, the algorithm developed in this work is applied to train the network using a small training set to determine which pathways in these networks interact and can maximize therapeutic effects.
The pruned GMDH is used to train a network on inputs of drugs presented one-at-time and predict the output when the input set includes pairs-at-a-time, three at a time etc. This algorithm was successful in developing the network for an input set of drugs which was limited to one-at-a-time. The algorithm was then used to train the network when the input set was changed to one-at-a-time and pairs-at-a-time, where it was able to predict the output for test set (includes drugs provided three-at-a-time, four-at-a-time etc) with an accuracy rate of 91%. The test results suggest that this approach may be of great value in the analysis of combination of drugs to produce maximized therapeutic effects.

REFERENCES:

1. Ivakhnenko, A.G. “Polynomial Theory of Complex Systems.” IEEE Transactions on Systems, Man, and Cybernetics, vol. 1, pp. 364-378, 1971
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3. Liebovitch L, Nicholas and Pandya A. S. “Developing Combinatorial Multi-Component Therapies (CMCT) of Drugs that are More Specific and Have Fewer Side Effects than Traditional One Drug Therapies”, pre-print, 2006
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