Hierarchical deep compartment modeling: A workflow to leverage machine learning and Bayesian inference for hierarchical pharmacometric modeling.

Population pharmacokinetic (PK) modeling serves as the cornerstone for understanding drug behavior within a specific population. It integrates subject covariates to elucidate the variability in PK parameters, thus enhancing predictive accuracy. However, covariate modeling within this framework can be intricate and time-consuming due to the often obscure structural relationship between covariates and PK parameters. Previous attempts, such as deep compartment modeling (DCM), aimed to streamline this process using machine learning techniques. Nonetheless, DCM fell short in assessing residual errors and interindividual variability (IIV), potentially leading to model misspecification and overfitting. Furthermore, DCM lacked the ability to quantify model uncertainty. To address these limitations, we introduce hierarchical deep compartment modeling (HDCM) as an advancement of DCM. HDCM harnesses machine learning to discern the interplay between covariates and PK parameters while simultaneously evaluating diverse levels of random effects and quantifying uncertainty through Bayesian inference. This tutorial provides a comprehensive application of the HDCM workflow using open-source Julia tools.

Making drugs from T cells: The quantitative pharmacology of engineered T cell therapeutics.

Engineered T cells have emerged as highly effective treatments for hematological cancers. Hundreds of clinical programs are underway in efforts to expand the efficacy, safety, and applications of this immuno-therapeutic modality. A primary challenge in developing these "living drugs" is the complexity of their pharmacology, as the drug product proliferates, differentiates, traffics between tissues, and evolves through interactions with patient immune systems. Using publicly available clinical data from Chimeric Antigen Receptor (CAR) T cells, we demonstrate how mathematical models can be used to quantify the relationships between product characteristics, patient physiology, pharmacokinetics and clinical outcomes. As scientists work to develop next-generation cell therapy products, mathematical models will be integral for contextualizing data and facilitating the translation of product designs to clinical strategy.

Deconvolution of clinical variance in CAR-T cell pharmacology and response.

Chimeric antigen receptor T cell (CAR-T) expansion and persistence vary widely among patients and predict both efficacy and toxicity. However, the mechanisms underlying clinical outcomes and patient variability are poorly defined. In this study, we developed a mathematical description of T cell responses wherein transitions among memory, effector and exhausted T cell states are coordinately regulated by tumor antigen engagement. The model is trained using clinical data from CAR-T products in different hematological malignancies and identifies cell-intrinsic differences in the turnover rate of memory cells and cytotoxic potency of effectors as the primary determinants of clinical response. Using a machine learning workflow, we demonstrate that product-intrinsic differences can accurately predict patient outcomes based on pre-infusion transcriptomes, and additional pharmacological variance arises from cellular interactions with patient tumors. We found that transcriptional signatures outperform T cell immunophenotyping as predictive of clinical response for two CD19-targeted CAR-T products in three indications, enabling a new phase of predictive CAR-T product development.

Virtual clinical trial simulations for a novel KRASG12C inhibitor (ASP2453) in non-small cell lung cancer.

KRAS is a small GTPase family protein that relays extracellular growth signals to cell nucleus. KRASG12C mutations lead to constitutive proliferation signaling and are prevalent across human cancers. ASP2453 is a novel, highly potent, and selective inhibitor of KRASG12C . Although preclinical data suggested impressive efficacy, it remains unclear whether ASP2453 will show more favorable clinical response compared to more advanced competitors, such as AMG 510. Here, we developed a quantitative systems pharmacology (QSP) model linking KRAS signaling to tumor growth in patients with non-small cell lung cancer. The model was parameterized using in vitro ERK1/2 phosphorylation and in vivo xenograft data for ASP2453. Publicly disclosed clinical data for AMG 510 were used to generate a virtual population, and tumor size changes in response to ASP2453 and AMG 510 were simulated. The QSP model predicted ASP2453 exhibits greater clinical response than AMG 510, supporting potential differentiation and critical thinking for clinical trials.

Reproducibility of Quantitative Systems Pharmacology Models: Current Challenges and Future Opportunities.

The provision of model code is required for publication in CPT: Pharmacometrics & Systems Pharmacology, enabling quantitative systems pharmacology (QSP) model availability. A searchable repository of published QSP models would enhance model accessibility. We assess the feasibility of establishing such a resource based on 18 QSP models published in this journal. However, because of the diversity of software platforms (nine), file formats, and functionality, such a resource is premature. We evaluated 12 of the models (those coded in R, PK-Sim/MoBi, and MATLAB) for functionality. Of the 12, only 4 were executable in that figures from the associated manuscript could be generated via a "run" script. Many researchers are aware of the challenges involved in repurposing published models. We offer some ideas to enable model sharing going forward, including annotation guidelines, standardized formats, and the inclusion of "run" scripts. If practitioners can agree to some minimum standards for the provision of model code, model reuse and extension would be accelerated.

A transcriptional MAPK Pathway Activity Score (MPAS) is a clinically relevant biomarker in multiple cancer types.

KRAS- and BRAF-mutant tumors are often dependent on MAPK signaling for proliferation and survival and thus sensitive to MAPK pathway inhibitors. However, clinical studies have shown that MEK inhibitors are not uniformly effective in these cancers indicating that mutational status of these oncogenes does not accurately capture MAPK pathway activity. A number of transcripts are regulated by this pathway and are recurrently identified in genome-based MAPK transcriptional signatures. To test whether the transcriptional output of only 10 of these targets could quantify MAPK pathway activity with potential predictive or prognostic clinical utility, we created a MAPK Pathway Activity Score (MPAS) derived from aggregated gene expression. In vitro, MPAS predicted sensitivity to MAPK inhibitors in multiple cell lines, comparable to or better than larger genome-based statistical models. Bridging in vitro studies and clinical samples, median MPAS from a given tumor type correlated with cobimetinib (MEK inhibitor) sensitivity of cancer cell lines originating from the same tissue type. Retrospective analyses of clinical datasets showed that MPAS was associated with the sensitivity of melanomas to vemurafenib (HR: 0.596) and negatively prognostic of overall or progression-free survival in both adjuvant and metastatic CRC (HR: 1.5 and 1.4), adrenal cancer (HR: 1.7), and HER2+ breast cancer (HR: 1.6). MPAS thus demonstrates potential clinical utility that warrants further exploration.

Correction: Combined MEK and ERK inhibition overcomes therapy-mediated pathway reactivation in RAS mutant tumors.

[This corrects the article DOI: 10.1371/journal.pone.0185862.].

Combined MEK and ERK inhibition overcomes therapy-mediated pathway reactivation in RAS mutant tumors.

Mitogen-activated protein kinase (MAPK) pathway dysregulation is implicated in >30% of all cancers, rationalizing the development of RAF, MEK and ERK inhibitors. While BRAF and MEK inhibitors improve BRAF mutant melanoma patient outcomes, these inhibitors had limited success in other MAPK dysregulated tumors, with insufficient pathway suppression and likely pathway reactivation. In this study we show that inhibition of either MEK or ERK alone only transiently inhibits the MAPK pathway due to feedback reactivation. Simultaneous targeting of both MEK and ERK nodes results in deeper and more durable suppression of MAPK signaling that is not achievable with any dose of single agent, in tumors where feedback reactivation occurs. Strikingly, combined MEK and ERK inhibition is synergistic in RAS mutant models but only additive in BRAF mutant models where the RAF complex is dissociated from RAS and thus feedback productivity is disabled. We discovered that pathway reactivation in RAS mutant models occurs at the level of CRAF with combination treatment resulting in a markedly more active pool of CRAF. However, distinct from single node targeting, combining MEK and ERK inhibitor treatment effectively blocks the downstream signaling as assessed by transcriptional signatures and phospho-p90RSK. Importantly, these data reveal that MAPK pathway inhibitors whose activity is attenuated due to feedback reactivation can be rescued with sufficient inhibition by using a combination of MEK and ERK inhibitors. The MEK and ERK combination significantly suppresses MAPK pathway output and tumor growth in vivo to a greater extent than the maximum tolerated doses of single agents, and results in improved anti-tumor activity in multiple xenografts as well as in two Kras mutant genetically engineered mouse (GEM) models. Collectively, these data demonstrate that combined MEK and ERK inhibition is functionally unique, yielding greater than additive anti-tumor effects and elucidates a highly effective combination strategy in MAPK-dependent cancer, such as KRAS mutant tumors.

Erratum: Clinical responses to ERK inhibition in BRAFV600E-mutant colorectal cancer predicted using a computational model.

[This corrects the article DOI: 10.1038/s41540-017-0016-1.].

Clinical responses to ERK inhibition in BRAFV600E-mutant colorectal cancer predicted using a computational model.

Approximately 10% of colorectal cancers harbor BRAFV600E mutations, which constitutively activate the MAPK signaling pathway. We sought to determine whether ERK inhibitor (GDC-0994)-containing regimens may be of clinical benefit to these patients based on data from in vitro (cell line) and in vivo (cell- and patient-derived xenograft) studies of cetuximab (EGFR), vemurafenib (BRAF), cobimetinib (MEK), and GDC-0994 (ERK) combinations. Preclinical data was used to develop a mechanism-based computational model linking cell surface receptor (EGFR) activation, the MAPK signaling pathway, and tumor growth. Clinical predictions of anti-tumor activity were enabled by the use of tumor response data from three Phase 1 clinical trials testing combinations of EGFR, BRAF, and MEK inhibitors. Simulated responses to GDC-0994 monotherapy (overall response rate = 17%) accurately predicted results from a Phase 1 clinical trial regarding the number of responding patients (2/18) and the distribution of tumor size changes ("waterfall plot"). Prospective simulations were then used to evaluate potential drug combinations and predictive biomarkers for increasing responsiveness to MEK/ERK inhibitors in these patients.

HER2+ Cancer Cell Dependence on PI3K vs. MAPK Signaling Axes Is Determined by Expression of EGFR, ERBB3 and CDKN1B.

Understanding the molecular pathways by which oncogenes drive cancerous cell growth, and how dependence on such pathways varies between tumors could be highly valuable for the design of anti-cancer treatment strategies. In this work we study how dependence upon the canonical PI3K and MAPK cascades varies across HER2+ cancers, and define biomarkers predictive of pathway dependencies. A panel of 18 HER2+ (ERBB2-amplified) cell lines representing a variety of indications was used to characterize the functional and molecular diversity within this oncogene-defined cancer. PI3K and MAPK-pathway dependencies were quantified by measuring in vitro cell growth responses to combinations of AKT (MK2206) and MEK (GSK1120212; trametinib) inhibitors, in the presence and absence of the ERBB3 ligand heregulin (NRG1). A combination of three protein measurements comprising the receptors EGFR, ERBB3 (HER3), and the cyclin-dependent kinase inhibitor p27 (CDKN1B) was found to accurately predict dependence on PI3K/AKT vs. MAPK/ERK signaling axes. Notably, this multivariate classifier outperformed the more intuitive and clinically employed metrics, such as expression of phospho-AKT and phospho-ERK, and PI3K pathway mutations (PIK3CA, PTEN, and PIK3R1). In both cell lines and primary patient samples, we observed consistent expression patterns of these biomarkers varies by cancer indication, such that ERBB3 and CDKN1B expression are relatively high in breast tumors while EGFR expression is relatively high in other indications. The predictability of the three protein biomarkers for differentiating PI3K/AKT vs. MAPK dependence in HER2+ cancers was confirmed using external datasets (Project Achilles and GDSC), again out-performing clinically used genetic markers. Measurement of this minimal set of three protein biomarkers could thus inform treatment, and predict mechanisms of drug resistance in HER2+ cancers. More generally, our results show a single oncogenic transformation can have differing effects on cell signaling and growth, contingent upon the molecular and cellular context.

Computational modeling of ERBB2-amplified breast cancer identifies combined ErbB2/3 blockade as superior to the combination of MEK and AKT inhibitors.

Crosstalk and compensatory circuits within cancer signaling networks limit the activity of most targeted therapies. For example, altered signaling in the networks activated by the ErbB family of receptors, particularly in ERBB2-amplified cancers, contributes to drug resistance. We developed a multiscale systems model of signaling networks in ERBB2-amplified breast cancer to quantitatively investigate relationships between biomarkers (markers of network activity) and combination drug efficacy. This model linked ErbB receptor family signaling to breast tumor growth through two kinase cascades: the PI3K/AKT survival pathway and the Ras/MEK/ERK growth and proliferation pathway. The model predicted molecular mechanisms of resistance to individual therapeutics. In particular, ERBB2-amplified breast cancer cells stimulated with the ErbB3 ligand heregulin were resistant to growth arrest induced by inhibitors of AKT and MEK or coapplication of two inhibitors of the receptor ErbB2 [Herceptin (trastuzumab) and Tykerb (lapatinib)]. We used model simulations to predict the response of ErbB2-positive breast cancer xenografts to combination therapies and verified these predictions in mice. Treatment with trastuzumab, lapatinib, and the ErbB3 inhibitor MM-111 was more effective in inhibiting tumor growth than the combination of AKT and MEK inhibitors and even induced tumor regression, indicating that targeting both ErbB3 and ErbB2 may be an improved therapeutic approach for ErbB2-positive breast cancer patients.

Creating and analyzing pathway and protein interaction compendia for modelling signal transduction networks.

BACKGROUND: Understanding the information-processing capabilities of signal transduction networks, how those networks are disrupted in disease, and rationally designing therapies to manipulate diseased states require systematic and accurate reconstruction of network topology. Data on networks central to human physiology, such as the inflammatory signalling networks analyzed here, are found in a multiplicity of on-line resources of pathway and interactome databases (Cancer CellMap, GeneGo, KEGG, NCI-Pathway Interactome Database (NCI-PID), PANTHER, Reactome, I2D, and STRING). We sought to determine whether these databases contain overlapping information and whether they can be used to construct high reliability prior knowledge networks for subsequent modeling of experimental data. RESULTS: We have assembled an ensemble network from multiple on-line sources representing a significant portion of all machine-readable and reconcilable human knowledge on proteins and protein interactions involved in inflammation. This ensemble network has many features expected of complex signalling networks assembled from high-throughput data: a power law distribution of both node degree and edge annotations, and topological features of a "bow tie" architecture in which diverse pathways converge on a highly conserved set of enzymatic cascades focused around PI3K/AKT, MAPK/ERK, JAK/STAT, NFκB, and apoptotic signaling. Individual pathways exhibit "fuzzy" modularity that is statistically significant but still involving a majority of "cross-talk" interactions. However, we find that the most widely used pathway databases are highly inconsistent with respect to the actual constituents and interactions in this network. Using a set of growth factor signalling networks as examples (epidermal growth factor, transforming growth factor-beta, tumor necrosis factor, and wingless), we find a multiplicity of network topologies in which receptors couple to downstream components through myriad alternate paths. Many of these paths are inconsistent with well-established mechanistic features of signalling networks, such as a requirement for a transmembrane receptor in sensing extracellular ligands. CONCLUSIONS: Wide inconsistencies among interaction databases, pathway annotations, and the numbers and identities of nodes associated with a given pathway pose a major challenge for deriving causal and mechanistic insight from network graphs. We speculate that these inconsistencies are at least partially attributable to cell, and context-specificity of cellular signal transduction, which is largely unaccounted for in available databases, but the absence of standardized vocabularies is an additional confounding factor. As a result of discrepant annotations, it is very difficult to identify biologically meaningful pathways from interactome networks a priori. However, by incorporating prior knowledge, it is possible to successively build out network complexity with high confidence from a simple linear signal transduction scaffold. Such reduced complexity networks appear suitable for use in mechanistic models while being richer and better justified than the simple linear pathways usually depicted in diagrams of signal transduction.

Rapid expansion of human hematopoietic stem cells by automated control of inhibitory feedback signaling.

Clinical hematopoietic transplantation outcomes are strongly correlated with the numbers of cells infused. Anticipated novel therapeutic implementations of hematopoietic stem cells (HSCs) and their derivatives further increase interest in strategies to expand HSCs ex vivo. A fundamental limitation in all HSC-driven culture systems is the rapid generation of differentiating cells and their secreted inhibitory feedback signals. Herein we describe an integrated computational and experimental strategy that enables a tunable reduction in the global levels and impact of paracrine signaling factors in an automated closed-system process by employing a controlled fed-batch media dilution approach. Application of this system to human cord blood cells yielded a rapid (12-day) 11-fold increase of HSCs with self-renewing, multilineage repopulating ability. These results highlight the marked improvements that control of feedback signaling can offer primary stem cell culture and demonstrate a clinically relevant rapid and relatively low culture volume strategy for ex vivo HSC expansion.

Dynamic interaction networks in a hierarchically organized tissue.

Intercellular (between cell) communication networks maintain homeostasis and coordinate regenerative and developmental cues in multicellular organisms. Despite the importance of intercellular networks in stem cell biology, their rules, structure and molecular components are poorly understood. Herein, we describe the structure and dynamics of intercellular and intracellular networks in a stem cell derived, hierarchically organized tissue using experimental and theoretical analyses of cultured human umbilical cord blood progenitors. By integrating high-throughput molecular profiling, database and literature mining, mechanistic modeling, and cell culture experiments, we show that secreted factor-mediated intercellular communication networks regulate blood stem cell fate decisions. In particular, self-renewal is modulated by a coupled positive-negative intercellular feedback circuit composed of megakaryocyte-derived stimulatory growth factors (VEGF, PDGF, EGF, and serotonin) versus monocyte-derived inhibitory factors (CCL3, CCL4, CXCL10, TGFB2, and TNFSF9). We reconstruct a stem cell intracellular network, and identify PI3K, Raf, Akt, and PLC as functionally distinct signal integration nodes, linking extracellular, and intracellular signaling. This represents the first systematic characterization of how stem cell fate decisions are regulated non-autonomously through lineage-specific interactions with differentiated progeny.

The AC133+CD38-, but not the rhodamine-low, phenotype tracks LTC-IC and SRC function in human cord blood ex vivo expansion cultures.

Phenotypic markers associated with human hematopoietic stem cells (HSCs) were developed and validated using uncultured cells. Because phenotype and function can be dissociated during culture, better markers to prospectively track and isolate HSCs in ex vivo cultures could be instrumental in advancing HSC-based therapies. Using an expansion system previously shown to increase hematopoietic progenitors and SCID-repopulating cells (SRCs), we demonstrated that the rhodamine-low phenotype was lost, whereas AC133 expression was retained throughout culture. Furthermore, the AC133(+)CD38(-) subpopulation was significantly enriched in long-term culture-initiating cells (LTC-IC) and SRCs after culture. Preculture and postculture analysis of total nucleated cell and LTC-IC number, and limiting dilution analysis in NOD/SCID mice, showed a 43-fold expansion of the AC133(+)CD38(-) subpopulation that corresponded to a 7.3-fold and 4.4-fold expansion of LTC-ICs and SRCs in this subpopulation, respectively. Thus, AC133(+)CD38(-) is an improved marker that tracks and enriches for LTC-IC and SRC in ex vivo cultures.

Cell-cell interaction networks regulate blood stem and progenitor cell fate.

Communication networks between cells and tissues are necessary for homeostasis in multicellular organisms. Intercellular (between cell) communication networks are particularly relevant in stem cell biology, as stem cell fate decisions (self-renewal, proliferation, lineage specification) are tightly regulated based on physiological demand. We have developed a novel mathematical model of blood stem cell development incorporating cell-level kinetic parameters as functions of secreted molecule-mediated intercellular networks. By relation to quantitative cellular assays, our model is capable of predictively simulating many disparate features of both normal and malignant hematopoiesis, relating internal parameters and microenvironmental variables to measurable cell fate outcomes. Through integrated in silico and experimental analyses, we show that blood stem and progenitor cell fate is regulated by cell-cell feedback, and can be controlled non-cell autonomously by dynamically perturbing intercellular signalling. We extend this concept by demonstrating that variability in the secretion rates of the intercellular regulators is sufficient to explain heterogeneity in culture outputs, and that loss of responsiveness to cell-cell feedback signalling is both necessary and sufficient to induce leukemic transformation in silico.