Journal of Theoretical Biology 248 (2007) 259–266 Optimization of interleukin-21 immunotherapeutic strategies Antonio Cappuccio 1 , Moran Elishmereni 1 , Zvia Agur à Institute for Medical Biomathematics (IMBM), P.O.B. 282, Hate’ena St. 10, Bene-Ataroth 60991, Israel Received 21 December 2006; received in revised form 11 May 2007; accepted 11 May 2007 Available online 18 May 2007 Abstract The recently discovered interleukin-21 (IL-21) shows strong tumor attenuation in preclinical studies, and is considered a promising cancer immunotherapy agent. Yet, to exploit its potential, therapeutic strategies must be designed to achieve adequate balance between several conflicting aspects. A mathematical model describing the IL-21-antitumor effects provided the basis for application of the optimization methodology, aimed at finding improved immunotherapeutic regimens. Both dosages and inter-dosing intervals were optimized while considering maximal efficacy, determined by reduction of tumor burden, and minimal toxicity, estimated by cumulative IL-21 doses applied. Simulations allowed to compute the optimal regimen and explore its dependence on the weights of the target function. Optimized schedules lead to substantial cancer regression even with relatively low drug concentrations. Collectively, administration times shifted towards treatment onset, and IL-21 intensities sequentially decreased. Interestingly, there was a certain window in which deviations in the total IL-21 dosage administered largely influenced tumor elimination. The findings emphasize the importance of early tumor detection and the critical consequence of the inter-dosing interval on therapeutic efficacy, as supported by similar research involving chemotherapy. Our work provides initial basis for identifying clinically applicable IL-21 therapeutic strategies with improved efficacy/toxicity ratios. r 2007 Elsevier Ltd. All rights reserved. Keywords: Cancer immunotherapy; Cytokine; Efficacy/toxicity ratio; Optimization; Ordinary differential equations 1. Introduction The design and evaluation of therapeutic regimens that maximize efficacy/toxicity ratios is a critical stage of drug development. However, the identification of adequate treatment strategies is a complicated matter. The wide spectrum of biological reactions induced by a specific therapeutic agent creates an intricate network of processes, thus simple biological intuition may not suffice for designing treatments that fully exploit the potential of a therapeutic agent. Commonly used ap- proaches of experimental trial and error in clinical evaluations are time and resource consuming, with no guarantee of success. Mathematical models may aid in rational design of drug administration. Such models provide a deeper under- standing of the dynamics involved in biological processes, and serve as a basis for implementing mathematical optimization techniques. Over the past 20 years or so, mathematical modeling has been oriented towards rational development and application of cancer treatment (Norton and Simon, 1977; Goldie and Coldman, 1979; Agur et al., 1988, 1992; Ubezio et al., 1994; Kirschner and Panetta, 1998; Skomorovski et al., 2003; Arakelyan et al., 2005; de Pillis et al., 2005, 2006). Optimization algorithms are natural methods within the growing biomathematical tool kit, for studying various aspects of disturbed biological environments. These methodologies have already been applied in the field of cancer chemotherapy (Acharya and Sundareshan, 1984; Swan, 1987, 1988, 1990; Pedreira and Vila, 1991; Swierniak, 1995, 1996; Boldrini and Costa, 2000; Swierniak et al., 2001; Agur et al., 2006) and cancer immunotherapy (de Pillis and Radunskaya, 2001; Burden et al., 2004), with minimization of tumor burden as their primary objective. Such studies have emphasized the importance of adequate selection of therapeutic times, ARTICLE IN PRESS www.elsevier.com/locate/yjtbi 0022-5193/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2007.05.015 à Corresponding author. Tel.: +972 3 9733075; fax: +972 3 9733410. E-mail address: agur@imbm.org (Z. Agur). 1 These authors contributed equally to this manuscript.