A novel Bayesian generative approach for estimating tumor dynamics from published studies.

Tumor growth inhibition (TGI) modeling attempts to describe the time course changes in tumor size for patients undergoing cancer therapy. TGI models present several advantages over traditional exposure-response models that are based explicitly on clinical end points and have become a popular tool in the pharmacometrics community. Unfortunately, the data required to fit TGI models, namely longitudinal tumor measurements, are sparse or often not available in literature or publicly accessible databases. On the contrary, common end points such as progression-free survival (PFS) and objective response rate (ORR) are directly derived from longitudinal tumor measurements and are routinely published. To this end, a Bayesian generative model relating underlying tumor dynamics to summary PFS and ORR data is introduced to learn TGI model parameters using only published summary data. The parameterized model can describe the tumor dynamics, quantify treatment effect, and account for differences in the study population. The utility of this model is shown by applying it to several published studies, and learned parameters are combined to simulate an in silico trial of a novel combination therapy in a novel setting.

Mechanistic Pharmacokinetic/Pharmacodynamic Modeling in Support of a Patient-Convenient, Longer Dosing Interval for Carfilzomib, a Covalent Inhibitor of the Proteasome.

BACKGROUND: Carfilzomib is an irreversible second-generation proteasome inhibitor that has a short elimination half-life but much longer pharmacodynamic (PD) effect based on its irreversible mechanism of action, making it amenable to longer dosing intervals. A mechanistic pharmacokinetic/pharmacodynamic (PK/PD) model was built using a bottom-up approach, based on the mechanism of action of carfilzomib and the biology of the proteasome, to provide further evidence of the comparability of once-weekly and twice-weekly dosing. METHODS: The model was qualified using clinical data from the phase III ENDEAVOR study, where the safety and efficacy of bortezomib (a reversible proteasome inhibitor) and carfilzomib were compared. Simulations were performed to compare the average proteasome inhibition across five cycles of treatment for the 20/70 mg/m2 once-weekly (70 QW) and 20/56 mg/m2 twice-weekly (56 BIW) regimens. RESULTS: Results indicated that while 70 QW had a higher maximum concentration (Cmax) and lower steady-state area under the concentration-time curve (AUC) than 56 BIW, the average proteasome inhibition after five cycles of treatment between the regimens was comparable. Presumably, the higher Cmax of carfilzomib from 70 QW compensates for the lower overall AUC compared with 56 BIW, and hence 70 QW is expected to have comparable proteasome inhibition, and therefore comparable efficacy, to 56 BIW. The comparable model-predicted proteasome inhibition between 70 QW and 56 BIW also translated to comparable clinical response, in terms of overall response rate and progression-free survival. CONCLUSION: This work provides a framework for which mechanistic PK/PD modeling can be used to guide optimization of dosing intervals for therapeutics with significantly longer PD effects than PK, and help further justify patient-convenient, longer dosing intervals.

Computational Analysis of Cytokine Release Following Bispecific T-Cell Engager Therapy: Applications of a Logic-Based Model.

Bispecific T-cell engaging therapies harness the immune system to elicit an effective anticancer response. Modulating the immune activation avoiding potential adverse effects such as cytokine release syndrome (CRS) is a critical aspect to realizing the full potential of this therapy. The use of suitable exogenous intervention strategies to mitigate the CRS risk without compromising the antitumoral capability of bispecific antibody treatment is crucial. To this end, computational approaches can be instrumental to systematically exploring the effects of combining bispecific antibodies with CRS intervention strategies. Here, we employ a logical model to describe the action of bispecific antibodies and the complex interplay of various immune system components and use it to perform simulation experiments to improve the understanding of the factors affecting CRS. We performed a sensitivity analysis to identify the comedications that could ameliorate CRS without impairing tumor clearance. Our results agree with publicly available experimental data suggesting anti-TNF and anti-IL6 as possible co-treatments. Furthermore, we suggest anti-IFNγ as a suitable candidate for clinical studies.

Characterizing Pharmacokinetic-Pharmacodynamic Relationships and Efficacy of PI3Kδ Inhibitors in Respiratory Models of TH2 and TH1 Inflammation.

We leveraged a clinical pharmacokinetic (PK)/pharmacodynamics (PD)/efficacy relationship established with an oral phosphatidylinositol 3-kinase (PI3K)δ inhibitor (Idelalisib) in a nasal allergen challenge study to determine whether a comparable PK/PD/efficacy relationship with PI3Kδ inhibitors was observed in preclinical respiratory models of type 2 T helper cell (TH2) and type 1 T helper cell (TH1) inflammation. Results from an in vitro rat blood basophil (CD63) activation assay were used as a PD biomarker. IC50 values for PI3Kδ inhibitors, MSD-496486311, MSD-126796721, Idelalisib, and Duvelisib, were 1.2, 4.8, 0.8, and 0.5 µM. In the ovalbumin Brown Norway TH2 pulmonary inflammation model, all PI3Kδ inhibitors produced a dose-dependent inhibition of bronchoalveolar lavage eosinophils (maximum effect between 80% and 99%). In a follow-up experiment designed to investigate PK attributes [maximum (or peak) plasma concentration (Cmax), area under the curve (AUC), time on target (ToT)] that govern PI3Kδ efficacy, MSD-496486311 [3 mg/kg every day (QD) and 100 mg/kg QD] produced 16% and 93% inhibition of eosinophils, whereas doses (20 mg/kg QD, 10 mg/kg twice per day, and 3 mg/kg three times per day) produced 54% to 66% inhibition. Our profiling suggests that impact of PI3Kδ inhibitors on eosinophils is supported by a PK target with a ToT over the course of treatment close to the PD IC50 rather than strictly driven by AUC, Cmax, or Cmin (minimum blood plasma concentration) coverage. Additional studies in an Altenaria alternata rat model, a sheep Ascaris-sensitive sheep model, and a TH1-driven rat ozone exposure model did not challenge our hypothesis, suggesting that an IC50 level of TE (target engagement) sustained for 24 hours is required to produce efficacy in these traditional models. We conclude that the PK/PD observations in our animal models appear to align with clinical results associated with a TH2 airway disease.

Mathematical Model of Bone Remodeling Captures the Antiresorptive and Anabolic Actions of Various Therapies.

A better understanding of the molecular pathways regulating the bone remodeling process should help in the development of new antiresorptive regulators and anabolic regulators, that is, regulators of bone resorption and of bone formation. Understanding the mechanisms by which parathyroid hormone (PTH) influences bone formation and how it switches from anabolic to catabolic action is important for treating osteoporosis (Poole and Reeve in Curr Opin Pharmacol 5:612-617, 2005). In this paper we describe a mathematical model of bone remodeling that incorporates, extends, and integrates several models of particular aspects of this biochemical system (Cabal et al. in J Bone Miner Res 28(8):1830-1836, 2013; Lemaire et al. in J Theor Biol 229:293-309, 2004; Peterson and Riggs in Bone 46:49-63, 2010; Raposo et al. in J Clin Endocrinol Metab 87(9):4330-4340, 2002; Ross et al. in J Disc Cont Dyn Sys Series B 17(6):2185-2200, 2012). We plan to use this model as a bone homeostasis platform to develop anabolic and antiresorptive compounds. The model will allow us to test hypotheses about the dynamics of compounds and to test the potential benefits of combination therapies. At the core of the model is the idealized account of osteoclast and osteoblast signaling given by Lemaire et al. (J Theor Biol 229:293-309, 2004). We have relaxed some of their assumptions about the roles of osteoprotegerin, transforming growth factor [Formula: see text], and receptor activator of nuclear factor [Formula: see text]B ligand; we have devised more detailed models of the interactions of these species. We have incorporated a model of the effect of calcium sensing receptor antagonists on remodeling (Cabal et al. in J Bone Miner Res 28(8):1830-1836, 2013). We have also incorporated a basic model of the effects of vitamin D on calcium homeostasis. We have included a simple model of the mechanism proposed by Bellido et al. (2003), Ross et al. (J Disc Cont Dyn Sys Series B 17(6):2185-2200, 2012), of the influence of PTH on osteoblast apoptosis, a mechanism that accounts for the anabolic response to pulsatile PTH administration. Finally, we have devised a simple model of the administration and effects of bisphosphonates. The biomarkers in the model are procollagen type 1 amino-terminal propeptide and C-terminal telopeptide. Bone mineral density is the model's principal endpoint.

Preclinical Experimental and Mathematical Approaches for Assessing Effective Doses of Inhaled Drugs, Using Mometasone to Support Human Dose Predictions.

BACKGROUND: Understanding the relationship between dose, lung exposure, and drug efficacy continues to be a challenging aspect of inhaled drug development. An experimental inhalation platform was developed using mometasone furoate to link rodent lung exposure to its in vivo pharmacodynamic (PD) effects. METHODS: We assessed the effect of mometasone delivered directly to the lung in two different rodent PD models of lung inflammation. The data obtained were used to develop and evaluate a mathematical model to estimate drug dissolution, transport, distribution, and efficacy, following inhaled delivery in rodents and humans. RESULTS: Mometasone directly delivered to the lung, in both LPS and Alternaria alternata rat models, resulted in dose dependent inhibition of BALf cellular inflammation. The parameters for our mathematical model were calibrated to describe the observed lung and systemic exposure profiles of mometasone in humans and in animal models. We found that physicochemical properties, such as lung fluid solubility and lipophilicity, strongly influenced compound distribution and lung retention. CONCLUSIONS: Presently, we report on a novel and sophisticated mathematical model leading to improvements in a current inhaled drug development practices by providing a quantitative understanding of the relationship between PD effects and drug concentration in lungs.

A semimechanistic model of the time-course of release of PTH into plasma following administration of the calcilytic JTT-305/MK-5442 in humans.

JTT-305/MK-5442 is a calcium-sensing receptor (CaSR) allosteric antagonist being investigated for the treatment of osteoporosis. JTT-305/MK-5442 binds to CaSRs, thus preventing receptor activation by Ca(2+) . In the parathyroid gland, this results in the release of parathyroid hormone (PTH). Sharp spikes in PTH secretion followed by rapid returns to baseline are associated with bone formation, whereas sustained elevation in PTH is associated with bone resorption. We have developed a semimechanistic, nonpopulation model of the time-course relationship between JTT-305/MK-5442 and whole plasma PTH concentrations to describe both the secretion of PTH and the kinetics of its return to baseline levels. We obtained mean concentration data for JTT-305/MK-5442 and whole PTH from a multiple dose study in U.S. postmenopausal women at doses of 5, 10, 15, and 20 mg. We hypothesized that PTH is released from two separate sources: a reservoir that is released rapidly (within minutes) in response to reduction in Ca(2+) binding, and a second source released more slowly following hours of reduced Ca(2+) binding. We modeled the release rates of these reservoirs as maximum pharmacologic effect (Emax ) functions of JTT-305/MK-5442 concentration. Our model describes both the dose-dependence of PTH time of occurrence for maximum drug concentration (Tmax ) and maximum concentration of drug (Cmax ), and the extent and duration of the observed nonmonotonic return of PTH to baseline levels following JTT-305/MK-5442 administration.

Phase-locked signals elucidate circuit architecture of an oscillatory pathway.

This paper introduces the concept of phase-locking analysis of oscillatory cellular signaling systems to elucidate biochemical circuit architecture. Phase-locking is a physical phenomenon that refers to a response mode in which system output is synchronized to a periodic stimulus; in some instances, the number of responses can be fewer than the number of inputs, indicative of skipped beats. While the observation of phase-locking alone is largely independent of detailed mechanism, we find that the properties of phase-locking are useful for discriminating circuit architectures because they reflect not only the activation but also the recovery characteristics of biochemical circuits. Here, this principle is demonstrated for analysis of a G-protein coupled receptor system, the M3 muscarinic receptor-calcium signaling pathway, using microfluidic-mediated periodic chemical stimulation of the M3 receptor with carbachol and real-time imaging of resulting calcium transients. Using this approach we uncovered the potential importance of basal IP3 production, a finding that has important implications on calcium response fidelity to periodic stimulation. Based upon our analysis, we also negated the notion that the Gq-PLC interaction is switch-like, which has a strong influence upon how extracellular signals are filtered and interpreted downstream. Phase-locking analysis is a new and useful tool for model revision and mechanism elucidation; the method complements conventional genetic and chemical tools for analysis of cellular signaling circuitry and should be broadly applicable to other oscillatory pathways.

A computational approach to inferring cellular protein-binding affinities from quantitative fluorescence resonance energy transfer imaging.

Fluorescence resonance energy transfer (FRET) microscopy can measure the spatial distribution of protein interactions inside live cells. Such experiments give rise to complex data sets with many images of single cells, motivating data reduction and abstraction. In particular, determination of the value of the equilibrium dissociation constant (K(d)) will provide a quantitative measure of protein-protein interactions, which is essential to reconstructing cellular signaling networks. Here, we investigate the feasibility of using quantitative FRET imaging of live cells to estimate the local value of K(d) for two interacting labeled molecules. An algorithm is developed to infer the values of K(d) using the intensity of individual voxels of 3-D FRET microscopy images. The performance of our algorithm is investigated using synthetic test data, both in the absence and in the presence of endogenous (unlabeled) proteins. The influence of optical blurring caused by the microscope (confocal or wide field) and detection noise on the accuracy of K(d) inference is studied. We show that deconvolution of images followed by analysis of intensity data at local level can improve the estimate of K(d). Finally, the performance of this algorithm using cellular data on the interaction between yellow fluorescent protein-Rac and cyan fluorescent protein-PBD in mammalian cells is shown.

Quantitative inference of cellular parameters from microfluidic cell culture systems.

Microfluidic cell culture systems offer a convenient way to measure cell biophysical parameters in conditions close to the physiological environment. We demonstrate the application of a mathematical model describing the spatial distribution of nutrient and growth factor concentrations in inferring cellular oxygen uptake rates from experimental measurements. We use experimental measurements of oxygen concentrations in a poly(dimethylsiloxane) (PDMS) microreactor culturing human hepatocellular liver carcinoma cells (HepG2) to infer quantitative information on cellular oxygen uptake rates. We use a novel microchannel design to avoid the parameter correlation problem associated with simultaneous cellular uptake and diffusion of oxygen through the PDMS surface. We find that the cellular uptake of oxygen is dependent on the cell density and can be modeled using a logistic term in the Michaelis-Menten equation. Our results are significant not only for the development of novel assays to quantitatively infer cell response to stimuli, but also for the development, design, and optimization of novel in vitro systems for drug discovery and tissue engineering.

Quantitative measurement and control of oxygen levels in microfluidic poly(dimethylsiloxane) bioreactors during cell culture.

Microfluidic bioreactors fabricated from highly gas-permeable poly(dimethylsiloxane) (PDMS) materials have been observed, somewhat unexpectedly, to give rise to heterogeneous long term responses along the length of a perfused mammalian cell culture channel, reminiscent of physiologic tissue zonation that arises at least in part due to oxygen gradients. To develop a more quantitative understanding and enable better control of the physical-chemical mechanisms underlying cell biological events in such PDMS reactors, dissolved oxygen concentrations in the channel system were quantified in real time using fluorescence intensity and lifetime imaging of an oxygen sensitive dye, ruthenium tris(2,2'-dipyridyl) dichloride hexahydrate (RTDP). The data indicate that despite oxygen diffusion through PDMS, uptake of oxygen by cells inside the perfused PDMS microchannels induces an axial oxygen concentration gradient, with lower levels recorded in downstream regions. The oxygen concentration gradient generated by a balance of cellular uptake, convective transport by media flow, and permeation through PDMS in our devices ranged from 0.0003 (mg/l)/mm to 0.7 (mg/l)/mm. The existence of such steep gradients induced by cellular uptake can have important biological consequences. Results are consistent with our mathematical model and give insight into the conditions under which flux of oxygen through PDMS into the microchannels will or will not contribute significantly to oxygen delivery to cells and also provide a design tool to manipulate and control oxygen for cell culture and device engineering. The combination of computerized microfluidics, in situ oxygen sensing, and mathematical models opens new windows for microphysiologic studies utilizing oxygen gradients and low oxygen tensions.

Optical imaging in microfluidic bioreactors enables oxygen monitoring for continuous cell culture.

For the first time, a fluorescence lifetime calibration method for an oxygen-sensitive dye ruthenium tris(2,2'-dipyridyl) dichloride hexahydrate (RTDP) is applied to image oxygen levels in poly(dimethyl siloxane) (PDMS) bioreactors containing living C2C12 mouse myoblasts. PDMS microsystems are broadly used in bioengineering applications due to their biocompatibility and ease of handling. For these systems, oxygen concentrations are of significance and are likely to play an important role in cell behavior and gene expression. Fluorescence lifetime imaging microscopy (FLIM) bases image contrast on fluorophore excited state lifetimes, which reflect local biochemistry. Unique attributes of the widefield, time-domain FLIM system include tunable excitation (337.1 to 960 nm), large temporal dynamic range (> or =600 ps), high spatial resolution (1.4 microm), calibrated detection (0 to 300+/-8 microM of oxygen), and rapid data acquisition and processing times (10 s). Oxygen levels decrease with increasing cell densities and are consistent with model outcomes obtained by simulating bioreactor oxygen diffusion and cell proliferation. In single bioreactor loops, FLIM detects spatial heterogeneity in oxygen levels with variations as high as 20%. The fluorescence lifetime-based imaging approach we describe avoids intensity-based artifacts (including photobleaching and concentration variations) and provides a technique with high spatial discrimination for oxygen monitoring in continuous cell culture systems.

Model-based analysis and design of a microchannel reactor for tissue engineering.

Recently developed perfusion micro-bioreactors offer the promise of more physiologic in vitro systems for tissue engineering. Successful application of such bioreactors will require a method to characterize the bioreactor environment required to elicit desired cell function. We present a mathematical model to describe nutrient/growth factor transport and cell growth inside a microchannel bioreactor. Using the model, we first show that the nature of spatial gradients in nutrient concentration can be controlled by both design and operating conditions and are a strong function of cell uptake rates. Next, we extend our model to investigate the spatial distributions of cell-secreted soluble autocrine/paracrine growth factors in the bioreactor. We show that the convective transport associated with the continuous cell culture and possible media recirculation can significantly alter the concentration distribution of the soluble signaling molecules as compared to static culture experiments and hence needs special attention when adapting static culture protocols for the bioreactor. Further, using an unsteady state model, we find that spatial gradients in nutrient/growth factor concentrations can bring about spatial variations in the cell density distribution inside the bioreactor, which can result in lowered working volume of the bioreactor. Finally, we show that the nutrient and spatial limitations can dramatically affect the composition of a co-cultured cell population. Our results are significant for the development, design, and optimization of novel micro-channel systems for tissue engineering.