## 1 Introduction  
The second biggest cause of mortality worldwide for both men and women is cancer. In 2018, it was responsible for 9.6 million fatalities, or 13% of all deaths. In 2030, 13.1 million people are predicted to die from cancer worldwide [1]. The most popular method for treating disseminated or systemic malignancies is chemotherapy [2]. All chemotherapeutic drugs employ their cytotoxic effect by interfering with the cellular synthesis and/or the role of RNA, DNA, and the proteins that maintain cells' life. Thus, they have solemn side effects because of their non-specificity in killing cancer cells, rather than normal cells [2]. To overcome these problems, recent research involving life sciences and technologies has led to the introduction of new drug molecules, which are highly specific for definite cell targets (e.g., DNA, tubulin) present in both cancer and regular cells [3]. Currently, drug discovery research is directed towards targeting the key enzymes involved in the intracellular signal transduction pathway responsible for cancer cell differentiation and proliferation [4]. Among these drugs are those targeting kinases, particularly phosphoinositide 3-kinase (PI3K) and cyclin-dependent kinase (CDK). PI3K is a lipid kinase that is essential for intracellular signalling and its pathway is most prone to mutation. There are different catalytic subunits for PI3K which are PI3K\(\alpha\), PI3K\(\beta\), PI3K\(\delta\) and PI3K\(\gamma\). These enzymes are activated through cell membrane protein-tyrosine kinase receptors. Following their activation, PI3K subunits \(\alpha\), \(\beta\), and \(\delta\) catalyze the phosphorylation of phosphatidylinositol-4,5-bisphosphate to yield phosphatidylinositol-3,4,5-triphosphate. Consequently, protein kinase B (pKB/Akt) and the mammalian target of rapamycin (mTOR) protein-serine/threonine kinases are activated, and promote the growth, differentiation, and proliferation of the cell [5]. CDKs are serine/threonine kinases that are overexpressed in different variants of cancer. In response to various extracellular and intracellular signals, CDKs govern, manage, and control cell division as well as influence transcription. Three cell-cycle-related subfamilies (CDK1, CDK4, and CDK5) and five transcriptional subfamilies (CDK7, CDK8, CDK9, CDK11, and CDK20) encompass the CDK family. Deregulation of CDKs is a mutual character of several illnesses, including cancer, and inhibition of definite members by a drug has produced highly positive therapeutic outcomes [6]. Drugs targeting PI3K and CDKs are specific, potent, have minimum side effects, and have supremacy over regular chemotherapeutic drugs in the therapy of different types of cancer [7; 8; 9; 10; 11]. Duvelisib (DUV) and seliciclib (SEL) are important members of the chemotherapeutic drugs which exert their action by selective inhibition of PI3K and CDK, respectively. DUV (also known as IPI-145) is a small molecule and its chemical name is: 8-chloro-2-phenyl-3-[(15)-1-(7H-purin-6-ylamino) ethyl]isquinolin-1-one (Figure 1). It has a molecular formula of C\({}_{22}\)H\({}_{17}\)ClN\({}_{6}\)O and its molar mass is 416.86 g/mol [12]. DUV was granted approval by the FDA for the therapy of relapsed or refractory chronic lymphocytic leukemia/ small lymphocytic lymphoma, and follicular lymphoma. It can also be used to treat T-cell lymphoma, solid tumors, and non-Hodgkin's lymphoma. DUV inhibits both PI3K\(\delta\) and PI3K\(\gamma\) via potent ATP-competitive inhibition; however, it has higher affinity toward PI3K\(\delta\) over PI3K\(\gamma\)[13; 14; 15; 16]. SEL (also known as (R)-roscovitine and CY-202) is a small purine analogue molecule (Figure 1). The chemical name of SEL is (2R)-2-[(6-(benzylamino)-9-isopropyl-9H-purin-2-yl] amino)-1-butanol. The chemical formula of SEL is C\({}_{19}\)H\({}_{26}\)N\({}_{60}\) and its molecular weight is 354.45 [17].