Pharma Focus Asia

Is Convex Dose Dependence A Side Effect That Multiple Drug Treatment Causes?

Y-h. Taguchi, Professor, Chuo University

TurkiTurki, Assistant Professor, King Abdulaziz University

Convex dose dependence of gene expression is supposed to be an interaction of multiple drug doses although it can be also observed by single drug treatment. Proposed methods can distinguish those that multiple drug treatments cause from those caused by single dose treatment. It is very effective to identify genes targeted by drug treatments.

Monotonic dose dependence is often regarded as evidence that the drug is effective. It is supposed to be used as a criterion to seek genes whose expression is specifically affected. On the other hand, multiple dose treatment can cause more complicated dose dependence, e.g., convex. Excluding genes that exhibit non-monotonic (convex) dose dependence might be reasonable. Is it reasonable to seek genes that exhibit monotonic dose dependence with multiple drug treatments? The answer seems to be No.

Seeking an effective drug is always a complex problem. Starting from millions compounds, one can try to seek effective drugs to be useful for diseases. Even if some drug candidate compounds seemingly effective to a target disease were identified, we had better to be careful about. Then, it is often required that the observed effect is associated with dose dependence. Dose dependence means that the effects observed must be a function of dose. More amount of drug is used, the more the effect should be. Then the effect is often saturated as the amount of drugs exceeds some threshold values. This kind of behavior is regarded as evidence that the drug identified is really effective to the target disease.

Due to the recent development of high throughput technology of sequencing, it came possible to measure gene expression profiles for the various dose dependence. Then, it is natural to identify genes affected by drug treatment with checking expression of which genes exhibit dose dependence. However, since there are as many as a few tens thousands genes, accidental dose dependence that can occur with a probability as small as 0.0001 can happen. This makes it difficult to decide which genes are really affected by drug treatments.

If the multiple drugs were used, the situation is more complicated, since interaction between multiple doses might result in non-monotonic dose dependence (e.g. convex). Thus the question is, if we observe convex dose dependence of gene expression when multiple drugs were used, what it means. Is it an evidence of interaction of multiple drugs? Lukačišinand Bollenbach1 carefully investigated gene expression profiles under the multiple drug treatments and found that convex dose dependence universally appears independent of the combination of drugs. Thus, their answer is Yes; convex dose dependence can be caused by multiple drug treatments.

However, Taguchi and Turki2 have recently reanalysed their massive observations and concluded that the answer is always no. Taguchi has developed the method called tensor (TD) based unsupervised feature extraction (FE)3 that enables us to select a small number of genes within a huge number of genes even when a limited number of observations are available. Usually, the number of doses is at most a few tens whereas the number of genes is a few tens thousands as denoted in the above.  TD based unsupervised FE also can allow us to select genes that exhibit ANY kinds of dose dependence in gene expression when drugs are treated. Taguchi and Turki analysed gene expression of various combinations of drug treatment, not one by one but in an integrated manner using TD based unsupervised FE. Then they found that convex dependence is observed in multiple drug treatment as expected. Thus, apparently, Lukačišin and Bollenbach are seemingly right. But the story did not end at this point.

When Taguchi and Turki applied Principal Component Analysis (PCA) based unsupervised FE, which is variant of TD based unsupervised FE and is suitable to analyse gene expression not in an integrated manner one by one, to gene expression of genes to which single drug was treated, they also found convex dose dependence as well. This suggested that convex dose is not always the evidence of interaction between multiple doses. Thus people need to distinguish convex dose dependence caused by single drug treatment from that caused by multiple drug treatment. Otherwise, genes that exhibit convex dose dependence might be wrongly identified as those affected by complicated interaction between multiple drugs. At first, genes must be evaluated if they exhibit convex dose dependence upon single drug treatment. And only when they are not, genes are investigated if it exhibits convex dose dependence under the multiple drug treatment.

Although the history of drug discovery and dose dependency investigation are old, it is very recent that they are combined with the recently developed high throughput technology that can measure expression of a few tens thousands genes. At the moment, our knowledge about how gene expression of individual genes is affected by drug treatment is limited. However, it is a very important topic since drug discovery is a time consuming and expensive procedure. Many computer aided methods that can shorten the period and reduce the amount of money required were developed, none of them was fully successful. Usage of gene expression for drug discovery might open a new gate through which we can make breakthroughs through the difficulty of drug discovery. In order to overcome these difficulties, there are no shortcuts. We have to accumulate basic knowledge about the dose dependence of gene expression.


  1. MartinLukačišinand Tobias Bollenbach, Emergent Gene Expression Responses to Drug Combinations Predict Higher-Order Drug Interactions, Cell Systems, 9, (2019) 5, 423 - 433.e3
  2. Y-h. Taguchi andTurkiTurki,Novel method for the prediction of drug-drug Interaction based on gene expression profiles,European Journal of Pharmaceutical Sciences,Volume 160,(2021)105742,
  3. Unsupervised Feature Extraction Applied to Bioinformatics: A PCA Based and TD Based Approach, Springer International, (2020), ISBN 978-3-030-22455-4.
Y-h. Taguchi

Y-h. Taguchi obtained Dr. Sci. of Physics from Tokyo Institute of Technology. He has published papers in major journals, including Scientific Reports and PLoS ONE,a monograph from Springer International and is serving as academic editors in journals including PLoS ONE, BMC Medical Genomics and Frontiers in Genetics:RNA.


TurkiTurki received a PhD in computer science from the New Jersey Institute of Technology. He has published papers in journals, including Expert Systems with Applications, Knowledge-Based Systems, and PLoS ONE. Dr. Turki is an editorial board member of Computers in Biology and Medicine and Sustainable Computing: Informatics and Systems.

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