A new approach for prediction of tumor sensitivity to targeted drugs based on functional data

Background The success of targeted anti-cancer drugs are frequently hindered by the lack of knowledge of the individual pathway of the patient and the extreme data requirements on the estimation of the personalized genetic network of the patient’s tumor. The prediction of tumor sensitivity to targeted drugs remains a major challenge in the design of optimal therapeutic strategies. The current sensitivity prediction approaches are primarily based on genetic characterizations of the tumor sample. We propose a novel sensitivity prediction approach based on functional perturbation data that incorporates the drug protein interaction information and sensitivities to a training set of drugs with known targets. Results We illustrate the high prediction accuracy of our framework on synthetic data generated from the Kyoto Encyclopedia of Genes and Genomes (KEGG) and an experimental dataset of four canine osteosarcoma tumor cultures following application of 60 targeted small-molecule drugs. We achieve a low leave one out cross validation error of <10% for the canine osteosarcoma tumor cultures using a drug screen consisting of 60 targeted drugs. Conclusions The proposed framework provides a unique input-output based methodology to model a cancer pathway and predict the effectiveness of targeted anti-cancer drugs. This framework can be developed as a viable approach for personalized cancer therapy.


TIM Example
To explain the Target Inhibition Map (TIM), let us consider a simple example of a pathway as shown in figure 4(a). The downstream target K 3 can be activated by either of the upstream targets K 1 or K 2 . The tumor is in turn caused by the activation of K 3 . For this directional pathway, we will assume that K 1 and K 2 are activated by their own mutations or have latent activations. We note that the tumor proliferation (tumor activation) can be stopped by inhibiting K 3 or inhibiting both of K 1 and K 2 . We can consider this as two series blocks (Block1= {K 1 , K 2 } and Block2 = {K 3 }) that independently can reduce tumor proliferation.
Suppose Block1 can reduce tumor proliferation by 80% and Block 2 can reduce tumor proliferation by 70% , then we will consider that inhibition of both blocks simultaneously will reduce tumor proliferation by (1-(1-0.8)(1-0.7))*100= 94%. Note that we consider the sensitivity to be 1 -the ratio of tumor cells remaining after drug application as compared to without drug application. Thus 94% reduction of tumor cells produces a sensitivity of 0.94. Thus, if we consider the sensitivities for different combinations of target inhibitions, we will arrive at a truth table of the sort shown in table A.1. The continuous sensitivities have been binarized using a threshold of 0.5. Note that, it is not required to test all the possible 2 3 = 8 target combinations for arriving at the column of sensitivities. For instance, if we consider the binarized sensitivities and our experimental data shows that inhibition of K 1 , K 2 , K 3 = {0, 0, 1} produces a sensitivity of 1, then we know that K 1 , K 2 , K 3 = {1, 0, 1}; {0, 1, 1}; {1, 1, 1} will also have a sensitivity of 1. Thus, in this particular case, we can estimate the sensitivities of 4 possible target combinations based on a single experiment. Tumor Survival     Table B.2.
In this section, we analyze the prediction error resulting from each serial pathway block. Let us consider that a block has β targets. Usually the β will be ≤ 6. Let us consider that the training set consists of η samples that are independently selected based on the probability distribution f X1,X2,··· ,X β . We are interested in predicting the block sensitivity of a new sample with the following target inhibition profile V = y 1 , y 2 , · · · , y β where y i = 0 or 1 for i ∈ {1, 2, · · · , β}. Let the number of 1's in V be denoted by ω and 0's by β − ω. Let A denote the event that a sample x 1 , x 2 , · · · , x β selected based on the probability distribution f X1,X2,··· ,X β has the relation (x 1 ≤ y 1 ) ∧ (x 2 ≤ y 2 ) ∧ · · · (x β ≤ y β ) .
Then assuming X 1 ,. . . X β are identically and independently distributed with equal probability of selecting 1 or 0, we have Similarly, let B denote the event that a sample x 1 , x 2 , · · · , x β selected based on the probability distribution f X1,X2,··· ,X β has the relation (x 1 ≥ y 1 ) ∧ (x 2 ≥ y 2 ) ∧ · · · (x β ≥ y β ) and at least one x i > y i for i = 1, 2, · · · , β. Thus, The number of samples out of the training set that satisfies events A and B follows binomial distributions Binomial(η, P (A)) and Binomial(η, P (B)) respectively. Thus, the expected number of samples for events A and B are η * P (A) and η * P (B). As a numerical example, if number of samples η = 60 and block size β = 6 and for equal number of 1's ω = 3, then the expected number of samples for event A= 7.5 and for event B = 6.56. For this example, the number of samples in combined events A and B will always be greater than 14 for all ω's.
Next, let us estimate the error in prediction when we estimate based on maximum sensitivity among points in A and minimum sensitivity among points in B. We will consider that A and B contain n 1 and n 2 points respectively with n 1 + n 2 = λ. Let the sensitivities of the λ points be distributed uniformly in [0 1].
We will also add two more points 0, 0, · · · , 0 and 1, 1, · · · , 1 with sensitivities 0 and 1 respectively. Let the sorted λ + 2 sensitivities be 0 ≤ s 1 ≤ s 2 · · · ≤ s λ ≤ 1. Let us denote the maximum sensitivity among the n 1 points in A by Y l and the minimum sensitivity among the n 2 points in B by Y h . Based on biological constraints, the actual sensitivity for y 1 , y 2 , · · · , y β lies between Y l and Y h . Without any other information, we will consider that the actual sensitivity Y ac follows a uniform distribution f Yac between Y l and Y h . Thus if we consider a basic prediction of Y p = (Y l + Y h )/2 for our unknown sensitivity, the expected error in prediction for given For the sorted λ + 2 sensitivities 0 ≤ s 1 ≤ s 2 · · · ≤ s λ ≤ 1, E(s i ) − E(s i−1 ) = 1/(λ + 1). Thus the expected error for a given λ is E(|Y ac − Y p | |λ) = 1 4 * (λ+1) . To calculate the expected error based on the possibilities of λ, we note that λ follows a binomial distribution Binomial(η, P (A) + P (B)). Thus the expected error is We also have P (A) + P (B) = 2 ω +2 β−ω −1 2 β ≥ 1 2 β/2−1 − 1 2 β . As a numerical example, when P (A) + P (B) = 1 2 β/2−1 − 1 2 β and η = 100, then E(|Y ac − Y p |) = 0.0057, 0.0106, 0.0204 for β = 4, 6, 8 respectively. Thus we note that the sensitivities for each individual block can be predicted with high precision.

TIM Circuits
The inferred circuits for primary cultures Charley and Cora are shown in Figs D.2 and D.3 respectively.