Mathematical model of hormone sensitive prostate cancer treatment using leuprolide: A small step towards personalization.

In this paper we present a new version of a mathematical model of Elishmereni et al. describing androgen deprivation therapy (ADT) for hormone sensitive prostate cancer patients (HSPC). We first focus on the detail description of the model, and then we present mathematical analysis of the proposed model, starting from the simplified model without resistance and ending on the full model with two resistance mechanisms present. We make a step towards personalization proposing an underlying tumor growth law base on a cohort of patients from Mayo hospital. We conclude that the model is able to reflect reality, that is in clinical scenarios the level of testosterone in HSPC patients inevitably rises leading to the failure of ADT.

Accelerating the Development of Personalized Cancer Immunotherapy by Integrating Molecular Patients' Profiles with Dynamic Mathematical Models.

We review the evolution, achievements, and limitations of the current paradigm shift in medicine, from the "one-size-fits-all" model to "Precision Medicine." Precision, or personalized, medicine-tailoring the medical treatment to the personal characteristics of each patient-engages advanced statistical methods to evaluate the relationships between static patient profiling (e.g., genomic and proteomic), and a simple clinically motivated output (e.g., yes/no responder). Today, precision medicine technologies that have facilitated groundbreaking advances in oncology, notably in cancer immunotherapy, are approaching the limits of their potential, mainly due to the scarcity of methods for integrating genomic, proteomic and clinical patient information. A different approach to treatment personalization involves methodologies focusing on the dynamic interactions in the patient-disease-drug system, as portrayed in mathematical modeling. Achievements of this scientific approach, in the form of algorithms for predicting personal disease dynamics in individual patients under immunotherapeutic drugs, are reviewed as well. The contribution of the dynamic approaches to precision medicine is limited, at present, due to insufficient applicability and validation. Yet, the time is ripe for amalgamating together these two approaches, for maximizing their joint potential to personalize and improve cancer immunotherapy. We suggest the roadmap toward achieving this goal, technologically, and urge clinicians, pharmacologists, and computational biologists to join forces along the pharmaco-clinical track of this development.

Predicting time to castration resistance in hormone sensitive prostate cancer by a personalization algorithm based on a mechanistic model integrating patient data.

BACKGROUND: Prostate cancer (PCa) is a leading cause of cancer death of men worldwide. In hormone-sensitive prostate cancer (HSPC), androgen deprivation therapy (ADT) is widely used, but an eventual failure on ADT heralds the passage to the castration-resistant prostate cancer (CRPC) stage. Because predicting time to failure on ADT would allow improved planning of personal treatment strategy, we aimed to develop a predictive personalization algorithm for ADT efficacy in HSPC patients. METHODS: A mathematical mechanistic model for HSPC progression and treatment was developed based on the underlying disease dynamics (represented by prostate-specific antigen; PSA) as affected by ADT. Following fine-tuning by a dataset of ADT-treated HSPC patients, the model was embedded in an algorithm, which predicts the patient's time to biochemical failure (BF) based on clinical metrics obtained before or early in-treatment. RESULTS: The mechanistic model, including a tumor growth law with a dynamic power and an elaborate ADT-resistance mechanism, successfully retrieved individual time-courses of PSA (R(2) = 0.783). Using the personal Gleason score (GS) and PSA at diagnosis, as well as PSA dynamics from 6 months after ADT onset, and given the full ADT regimen, the personalization algorithm accurately predicted the individual time to BF of ADT in 90% of patients in the retrospective cohort (R(2) = 0.98). CONCLUSIONS: The algorithm we have developed, predicting biochemical failure based on routine clinical tests, could be especially useful for patients destined for short-lived ADT responses and quick progression to CRPC. Prospective studies must validate the utility of the algorithm for clinical decision-making.

Complex pattern of interleukin-11-induced inflammation revealed by mathematically modeling the dynamics of C-reactive protein.

Inflammation underlies many diseases and is an undesired effect of several therapy modalities. Biomathematical modeling can help unravel the complex inflammatory processes and the mechanisms triggering their emergence. We developed a model for induction of C-reactive protein (CRP), a clinically reliable marker of inflammation, by interleukin (IL)-11, an approved cytokine for treatment of chemotherapy-induced thrombocytopenia. Due to paucity of information on the mechanisms underlying inflammation-induced CRP dynamics, our model was developed by systematically evaluating several models for their ability to retrieve variable CRP profiles observed in IL-11-treated breast cancer patients. The preliminary semi-mechanistic models were designed by non-linear mixed-effects modeling, and were evaluated by various performance criteria, which test goodness-of-fit, parsimony and uniqueness. The best-performing model, a robust population model with minimal inter-individual variability, uncovers new aspects of inflammation dynamics. It shows that CRP clearance is a nonlinear self-controlled process, indicating an adaptive anti-inflammatory reaction in humans. The model also reveals a dual IL-11 effect on CRP elevation, whereby the drug has not only a potent immediate influence on CRP incline, but also a long-term influence inducing elevated CRP levels for several months. Consistent with this, model simulations suggest that periodic IL-11 therapy may result in prolonged low-grade (chronic) inflammation post treatment. Future application of the model can therefore help design improved IL-11 regimens with minimized long-term CRP toxicity. Our study illuminates the dynamics of inflammation and its control, and provides a prototype for progressive modeling of complex biological processes in the medical realm and beyond.

Complex 2B4 regulation of mast cells and eosinophils in murine allergic inflammation.

The cell surface molecule 2B4 (CD244) is an important regulator of lymphocyte activation, and its role in antiviral immunity and lymphoproliferative disorders is well established. Although it is also expressed on mast cells (MCs) and eosinophils (Eos), the functions of 2B4 on these allergy-orchestrating cells remain unclear. We therefore investigated the role of 2B4 on murine MCs and Eos, particularly how this molecule affects allergic and nonallergic inflammatory processes involving these effector cells. Experiments in bone marrow-derived cultures revealed an inhibitory effect for 2B4 in MC degranulation, but also an opposing stimulatory effect in eosinophil migration and delayed activation. Murine disease models supported the dual 2B4 function: In 2B4-/- mice with nonallergic peritonitis and mild atopic dermatitis (AD), modest infiltrates of Eos into the peritoneum and skin (respectively) confirmed that 2B4 boosts eosinophil trafficking. In a chronic AD model, 2B4-/- mice showed overdegranulated MCs, confirming the inhibiting 2B4 effect on MC activation. This multifunctional 2B4 profile unfolded in inflammation resembles a similar mixed effect of 2B4 in natural killer cells. Taken together, our findings provide evidence for physiological 2B4 stimulatory/inhibitory effects in MCs and Eos, pointing to a complex role for 2B4 in allergy.

Personalizing oncology treatments by predicting drug efficacy, side-effects, and improved therapy: mathematics, statistics, and their integration.

Despite its great promise, personalized oncology still faces many hurdles, and it is increasingly clear that targeted drugs and molecular biomarkers alone yield only modest clinical benefit. One reason is the complex relationships between biomarkers and the patient's response to drugs, obscuring the true weight of the biomarkers in the overall patient's response. This complexity can be disentangled by computational models that integrate the effects of personal biomarkers into a simulator of drug-patient dynamic interactions, for predicting the clinical outcomes. Several computational tools have been developed for personalized oncology, notably evidence-based tools for simulating pharmacokinetics, Bayesian-estimated tools for predicting survival, etc. We describe representative statistical and mathematical tools, and discuss their merits, shortcomings and preliminary clinical validation attesting to their potential. Yet, the individualization power of mathematical models alone, or statistical models alone, is limited. More accurate and versatile personalization tools can be constructed by a new application of the statistical/mathematical nonlinear mixed effects modeling (NLMEM) approach, which until recently has been used only in drug development. Using these advanced tools, clinical data from patient populations can be integrated with mechanistic models of disease and physiology, for generating personal mathematical models. Upon a more substantial validation in the clinic, this approach will hopefully be applied in personalized clinical trials, P-trials, hence aiding the establishment of personalized medicine within the main stream of clinical oncology.

Reconsidering the paradigm of cancer immunotherapy by computationally aided real-time personalization.

Although therapeutic vaccination often induces markers of tumor-specific immunity, therapeutic responses remain rare. An improved understanding of patient-specific dynamic interactions of immunity and tumor progression, combined with personalized application of immune therapeutics would increase the efficacy of immunotherapy. Here, we developed a method to predict and enhance the individual response to immunotherapy by using personalized mathematical models, constructed in the early phase of treatment. Our approach includes an iterative real-time in-treatment evaluation of patient-specific parameters from the accruing clinical data, construction of personalized models and their validation, model-based simulation of subsequent response to ongoing therapy, and suggestion of potentially more effective patient-specific modified treatment. Using a mathematical model of prostate cancer immunotherapy, we applied our model to data obtained in a clinical investigation of an allogeneic whole-cell therapeutic prostate cancer vaccine. Personalized models for the patients who responded to treatment were derived and validated by data collected before treatment and during its early phase. Simulations, based on personalized models, suggested that an increase in vaccine dose and administration frequency would stabilize the disease in most patients. Together, our findings suggest that application of our method could facilitate development of a new paradigm for studies of in-treatment personalization of the immune agent administration regimens (P-trials), with treatment modifications restricted to an approved range, resulting in more efficacious immunotherapies.

An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin-21 regimens validated prospectively for mouse solid cancers.

Interleukin (IL)-21 is an attractive antitumor agent with potent immunomodulatory functions. Yet thus far, the cytokine has yielded only partial responses in solid cancer patients, and conditions for beneficial IL-21 immunotherapy remain elusive. The current work aims to identify clinically-relevant IL-21 regimens with enhanced efficacy, based on mathematical modeling of long-term antitumor responses. For this purpose, pharmacokinetic (PK) and pharmacodynamic (PD) data were acquired from a preclinical study applying systemic IL-21 therapy in murine solid cancers. We developed an integrated disease/PK/PD model for the IL-21 anticancer response, and calibrated it using selected "training" data. The accuracy of the model was verified retrospectively under diverse IL-21 treatment settings, by comparing its predictions to independent "validation" data in melanoma and renal cell carcinoma-challenged mice (R(2)>0.90). Simulations of the verified model surfaced important therapeutic insights: (1) Fractionating the standard daily regimen (50 µg/dose) into a twice daily schedule (25 µg/dose) is advantageous, yielding a significantly lower tumor mass (45% decrease); (2) A low-dose (12 µg/day) regimen exerts a response similar to that obtained under the 50 µg/day treatment, suggestive of an equally efficacious dose with potentially reduced toxicity. Subsequent experiments in melanoma-bearing mice corroborated both of these predictions with high precision (R(2)>0.89), thus validating the model also prospectively in vivo. Thus, the confirmed PK/PD model rationalizes IL-21 therapy, and pinpoints improved clinically-feasible treatment schedules. Our analysis demonstrates the value of employing mathematical modeling and in silico-guided design of solid tumor immunotherapy in the clinic.

CD48: A co-stimulatory receptor of immunity.

The CD48 molecule is a glycosyl-phosphatidyl-inositol (GPI)-anchored cell-surface protein of the CD2 family of molecules. Originally described on virally-induced B cells, CD48 has been found on various hematopoietic cells, and its expression is regulated by viral and bacterial products and immune-associated proteins. CD48 binds CD2 and other molecules, yet its high-affinity ligand in both mouse and human systems is 2B4. Despite its lack of an intracellular domain, stimulation of CD48 induces rearrangement of signaling factors in lipid rafts, Lck-kinase activity, and tyrosine phosphorylation. As an adhesion and co-stimulatory molecule, CD48 induces numerous effects in B and T lymphocytes, natural killer cells, mast cells, and eosinophils. Some of these depend upon cell-cell interactions via 2B4-CD48 binding. The structural and phenotypic characteristics of CD48, and its role in physiological and pathophysiological processes, are reviewed herein. Possible CD48-based applications for immune-impaired and inflammatory disorders are discussed as well.

Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models.

BACKGROUND: Therapeutic vaccination against disseminated prostate cancer (PCa) is partially effective in some PCa patients. We hypothesized that the efficacy of treatment will be enhanced by individualized vaccination regimens tailored by simple mathematical models. METHODOLOGY/PRINCIPAL FINDINGS: We developed a general mathematical model encompassing the basic interactions of a vaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole-cell vaccine. For model validation in the absence of any other pertinent marker, we used the clinically measured changes in prostate-specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were divided into each patient's training set and his validation set. The training set, used for model personalization, contained the patient's initial sequence of PSA levels; the validation set contained his subsequent PSA data points. Personalized models were simulated to predict changes in tumor burden and PSA levels and predictions were compared to the validation set. The model accurately predicted PSA levels over the entire measured period in 12 of the 15 vaccination-responsive patients (the coefficient of determination between the predicted and observed PSA values was R(2) = 0.972). The model could not account for the inconsistent changes in PSA levels in 3 of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. Personalized regimens predicted to enhance the effects of therapy differed among the patients. CONCLUSIONS/SIGNIFICANCE: Using a few initial measurements, we constructed robust patient-specific models of PCa immunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value and feasibility of individualized model-suggested immunotherapy protocols.

Ultrastructural evidence for human mast cell-eosinophil interactions in vitro.

We have hypothesized that mast cells (MC) and eosinophils (Eos), the main effectors of allergy, can form an effector unit. These cells co-exist in the inflamed tissues during the late and chronic stages of allergy and have been shown to be capable of influencing each other's survival and activity via soluble mediators. We have recently described couples of receptor-ligands that are expressed on either/both of these cells and that imply a physical interaction. In this study, we have investigated the existence of short-term (60 min) in vitro interactions between human peripheral blood Eos and cord-blood-derived MC by transmission electron microscopy. We have found that MC and Eos adhere to each other; the lipid body content and the granule morphology of co-cultured MC and Eos, respectively, are altered, and the level of Eos peroxidase (EPO) released by co-cultured Eos is elevated. Moreover, the transfer of EPO from Eos to MC and tryptase from MC to Eos has been observed. Our results thus indicate that, when co-cultured, MC and Eos show signs of physical contact and of reciprocal activation. This is the first in vitro evidence of functional physical interactions between human MC and Eos, interactions that might also occur in vivo during allergic diseases.

DNAM-1: an amplifier of immune responses as a therapeutic target in various disorders.

The co-stimulatory adhesion molecule DNAX accessory molecule 1 (DNAM-1) is a functional glycoprotein expressed on immune cells, such as natural killer and T-cells. It is activated upon interaction with its biological ligands, the poliovirus receptor and nectin-2. Signaling cascades involving stimulation of DNAM-1 lead to various biological responses, including target cell lysis and immune cell activation. Thus, DNAM-1 appears to be an integral molecule in immune responses in cancer, allergic inflammatory disorders and autoimmune diseases. The structure of DNAM-1, its mechanism of action and its effects in pathological scenarios are discussed.

Optimization of interleukin-21 immunotherapeutic strategies.

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.

Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model.

The newly characterized interleukin (IL)-21 plays a central role in the transition from innate immunity to adaptive immunity and shows substantial tumor regression in mice. IL-21 is now developed as a cancer immunotherapeutic drug, but conditions for efficacious therapy, and the conflicting immunostimulatory and immunoinhibitory influence of the cytokine, are yet to be defined. We studied the effects of IL-21 on tumor eradication in a mathematical model focusing on natural killer (NK) cell-mediated and CD8+ T-cell-mediated lysis of tumor cells. Model parameters were estimated using results in tumor-bearing mice treated with IL-21 via cytokine gene therapy (CGT), hydrodynamics-based gene delivery (HGD), or standard interval dosing (SID). Our model accurately retrieved experimental growth dynamics in the nonimmunogenic B16 melanoma and the immunogenic MethA and MCA205 fibrosarcomas, showing a strong dependence of the NK-cell/CD8+ T-cell balance on tumor immunogenicity. Moreover, in melanoma, simulations of CGT-like dosing regimens, dynamically determined according to tumor mass changes, resulted in efficient disease elimination. In contrast, in fibrosarcoma, such a strategy was not superior to that of fixed dosing regimens, HGD or SID. Our model supports clinical use of IL-21 as a potent stimulator of cellular immunity against cancer, and suggests selecting the immunotherapy strategy according to tumor immunogenicity. Nonimmunogenic tumors, but not highly immunogenic tumors, should be controlled by IL-21 dosing, which depends on tumor mass at the time of administration. This method imitates, yet amplifies, the natural anticancer immune response rather than accelerates only one of the response arms in an unbalanced manner.