Mathematical Modeling Unveils Optimization Strategies for Targeted Radionuclide Therapy of Blood Cancers.

Targeted radionuclide therapy is based on injections of cancer-specific molecules conjugated with radioactive nuclides. Despite the specificity of this treatment, it is not devoid of side-effects limiting its use and is especially harmful for rapidly proliferating organs well perfused by blood, like bone marrow. Optimization of radioconjugates administration accounting for toxicity constraints can increase treatment efficacy. Based on our experiments on disseminated multiple myeloma mouse model treated by 225Ac-DOTA-daratumumab, we developed a mathematical model which investigation highlighted the following principles for optimization of targeted radionuclide therapy. 1) Nuclide to antibody ratio importance. The density of radioconjugates on cancer cells determines the density of radiation energy deposited in them. Low labeling ratio as well as accumulation of unlabeled antibodies and antibodies attached to decay products in the bloodstream can mitigate cancer radiation damage due to excessive occupation of specific receptors by antibodies devoid of radioactive nuclides. 2) Cancer binding capacity-based dosing. The rate of binding of drug to cancer cells depends on the total number of their specific receptors, which therefore can be estimated from the pharmacokinetic curve of diagnostic radioconjugates. Injection of doses significantly exceeding cancer binding capacity should be avoided since radioconjugates remaining in the bloodstream have negligible efficacy to toxicity ratio. 3) Particle range-guided multi-dosing. The use of short-range particle emitters and high-affinity antibodies allows for robust treatment optimization via initial saturation of cancer binding capacity, enabling redistribution of further injected radioconjugates and deposited dose towards still viable cells that continue expressing specific receptors.

Designing combination therapies for cancer treatment: application of a mathematical framework combining CAR T-cell immunotherapy and targeted radionuclide therapy.

Introduction: Cancer combination treatments involving immunotherapies with targeted radiation therapy are at the forefront of treating cancers. However, dosing and scheduling of these therapies pose a challenge. Mathematical models provide a unique way of optimizing these therapies. Methods: Using a preclinical model of multiple myeloma as an example, we demonstrate the capability of a mathematical model to combine these therapies to achieve maximum response, defined as delay in tumor growth. Data from mice studies with targeted radionuclide therapy (TRT) and chimeric antigen receptor (CAR)-T cell monotherapies and combinations with different intervals between them was used to calibrate mathematical model parameters. The dependence of progression-free survival (PFS), overall survival (OS), and the time to minimum tumor burden on dosing and scheduling was evaluated. Different dosing and scheduling schemes were evaluated to maximize the PFS and optimize timings of TRT and CAR-T cell therapies. Results: Therapy intervals that were too close or too far apart are shown to be detrimental to the therapeutic efficacy, as TRT too close to CAR-T cell therapy results in radiation related CAR-T cell killing while the therapies being too far apart result in tumor regrowth, negatively impacting tumor control and survival. We show that splitting a dose of TRT or CAR-T cells when administered in combination is advantageous only if the first therapy delivered can produce a significant benefit as a monotherapy. Discussion: Mathematical models are crucial tools for optimizing the delivery of cancer combination therapy regimens with application along the lines of achieving cure, maximizing survival or minimizing toxicity.

Model discovery approach enables noninvasive measurement of intra-tumoral fluid transport in dynamic MRI.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a routine method to noninvasively quantify perfusion dynamics in tissues. The standard practice for analyzing DCE-MRI data is to fit an ordinary differential equation to each voxel. Recent advances in data science provide an opportunity to move beyond existing methods to obtain more accurate measurements of fluid properties. Here, we developed a localized convolutional function regression that enables simultaneous measurement of interstitial fluid velocity, diffusion, and perfusion in 3D. We validated the method computationally and experimentally, demonstrating accurate measurement of fluid dynamics in situ and in vivo. Applying the method to human MRIs, we observed tissue-specific differences in fluid dynamics, with an increased fluid velocity in breast cancer as compared to brain cancer. Overall, our method represents an improved strategy for studying interstitial flows and interstitial transport in tumors and patients. We expect that our method will contribute to the better understanding of cancer progression and therapeutic response.

Structural and practical identifiability of contrast transport models for DCE-MRI.

Contrast transport models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

Locoregional delivery of IL-13Rα2-targeting CAR-T cells in recurrent high-grade glioma: a phase 1 trial.

Chimeric antigen receptor T cell (CAR-T) therapy is an emerging strategy to improve treatment outcomes for recurrent high-grade glioma, a cancer that responds poorly to current therapies. Here we report a completed phase I trial evaluating IL-13Rα2-targeted CAR-T cells in 65 patients with recurrent high-grade glioma, the majority being recurrent glioblastoma (rGBM). Primary objectives were safety and feasibility, maximum tolerated dose/maximum feasible dose and a recommended phase 2 dose plan. Secondary objectives included overall survival, disease response, cytokine dynamics and tumor immune contexture biomarkers. This trial evolved to evaluate three routes of locoregional T cell administration (intratumoral (ICT), intraventricular (ICV) and dual ICT/ICV) and two manufacturing platforms, culminating in arm 5, which utilized dual ICT/ICV delivery and an optimized manufacturing process. Locoregional CAR-T cell administration was feasible and well tolerated, and as there were no dose-limiting toxicities across all arms, a maximum tolerated dose was not determined. Probable treatment-related grade 3+ toxicities were one grade 3 encephalopathy and one grade 3 ataxia. A clinical maximum feasible dose of 200 × 106 CAR-T cells per infusion cycle was achieved for arm 5; however, other arms either did not test or achieve this dose due to manufacturing feasibility. A recommended phase 2 dose will be refined in future studies based on data from this trial. Stable disease or better was achieved in 50% (29/58) of patients, with two partial responses, one complete response and a second complete response after additional CAR-T cycles off protocol. For rGBM, median overall survival for all patients was 7.7 months and for arm 5 was 10.2 months. Central nervous system increases in inflammatory cytokines, including IFNγ, CXCL9 and CXCL10, were associated with CAR-T cell administration and bioactivity. Pretreatment intratumoral CD3 T cell levels were positively associated with survival. These findings demonstrate that locoregional IL-13Rα2-targeted CAR-T therapy is safe with promising clinical activity in a subset of patients. ClinicalTrials.gov Identifier: NCT02208362 .

State-transition modeling of blood transcriptome predicts disease evolution and treatment response in chronic myeloid leukemia.

Chronic myeloid leukemia (CML) is initiated and maintained by BCR::ABL which is clinically targeted using tyrosine kinase inhibitors (TKIs). TKIs can induce long-term remission but are also not curative. Thus, CML is an ideal system to test our hypothesis that transcriptome-based state-transition models accurately predict cancer evolution and treatment response. We collected time-sequential blood samples from tetracycline-off (Tet-Off) BCR::ABL-inducible transgenic mice and wild-type controls. From the transcriptome, we constructed a CML state-space and a three-well leukemogenic potential landscape. The potential's stable critical points defined observable disease states. Early states were characterized by anti-CML genes opposing leukemia; late states were characterized by pro-CML genes. Genes with expression patterns shaped similarly to the potential landscape were identified as drivers of disease transition. Re-introduction of tetracycline to silence the BCR::ABL gene returned diseased mice transcriptomes to a near healthy state, without reaching it, suggesting parts of the transition are irreversible. TKI only reverted the transcriptome to an intermediate disease state, without approaching a state of health; disease relapse occurred soon after treatment. Using only the earliest time-point as initial conditions, our state-transition models accurately predicted both disease progression and treatment response, supporting this as a potentially valuable approach to time clinical intervention, before phenotypic changes become detectable.

A novel class of inhibitors that disrupts the stability of integrin heterodimers identified by CRISPR-tiling-instructed genetic screens.

The plasma membrane is enriched for receptors and signaling proteins that are accessible from the extracellular space for pharmacological intervention. Here we conducted a series of CRISPR screens using human cell surface proteome and integrin family libraries in multiple cancer models. Our results identified ITGAV (integrin αV) and its heterodimer partner ITGB5 (integrin ß5) as the essential integrin α/ß pair for cancer cell expansion. High-density CRISPR gene tiling further pinpointed the integral pocket within the ß-propeller domain of ITGAV for integrin αVß5 dimerization. Combined with in silico compound docking, we developed a CRISPR-Tiling-Instructed Computer-Aided (CRISPR-TICA) pipeline for drug discovery and identified Cpd_AV2 as a lead inhibitor targeting the ß-propeller central pocket of ITGAV. Cpd_AV2 treatment led to rapid uncoupling of integrin αVß5 and cellular apoptosis, providing a unique class of therapeutic action that eliminates the integrin signaling via heterodimer dissociation. We also foresee the CRISPR-TICA approach to be an accessible method for future drug discovery studies.

Systems profiling reveals recurrently dysregulated cytokine signaling responses in ER+ breast cancer patients' blood.

Cytokines mediate cell-to-cell communication across the immune system and therefore are critical to immunosurveillance in cancer and other diseases. Several cytokines show dysregulated abundance or signaling responses in breast cancer, associated with the disease and differences in survival and progression. Cytokines operate in a coordinated manner to affect immune surveillance and regulate one another, necessitating a systems approach for a complete picture of this dysregulation. Here, we profiled cytokine signaling responses of peripheral immune cells from breast cancer patients as compared to healthy controls in a multidimensional manner across ligands, cell populations, and responsive pathways. We find alterations in cytokine responsiveness across pathways and cell types that are best defined by integrated signatures across dimensions. Alterations in the abundance of a cytokine's cognate receptor do not explain differences in responsiveness. Rather, alterations in baseline signaling and receptor abundance suggesting immune cell reprogramming are associated with altered responses. These integrated features suggest a global reprogramming of immune cell communication in breast cancer.

State-transition Modeling of Blood Transcriptome Predicts Disease Evolution and Treatment Response in Chronic Myeloid Leukemia.

Chronic myeloid leukemia (CML) is initiated and maintained by BCR::ABL which is clinically targeted using tyrosine kinase inhibitors (TKIs). TKIs can induce long-term remission but are also not curative. Thus, CML is an ideal system to test our hypothesis that transcriptome-based state-transition models accurately predict cancer evolution and treatment response. We collected time-sequential blood samples from tetracycline-off (Tet-Off) BCR::ABL-inducible transgenic mice and wild-type controls. From the transcriptome, we constructed a CML state-space and a three-well leukemogenic potential landscape. The potential's stable critical points defined observable disease states. Early states were characterized by anti-CML genes opposing leukemia; late states were characterized by pro-CML genes. Genes with expression patterns shaped similarly to the potential landscape were identified as drivers of disease transition. Re-introduction of tetracycline to silence the BCR::ABL gene returned diseased mice transcriptomes to a near healthy state, without reaching it, suggesting parts of the transition are irreversible. TKI only reverted the transcriptome to an intermediate disease state, without approaching a state of health; disease relapse occurred soon after treatment. Using only the earliest time-point as initial conditions, our state-transition models accurately predicted both disease progression and treatment response, supporting this as a potentially valuable approach to time clinical intervention even before phenotypic changes become detectable.

Neuroprotective potential of intranasally delivered L-myc immortalized human neural stem cells in female rats after a controlled cortical impact injury.

Efficacious stem cell-based therapies for traumatic brain injury (TBI) depend on successful delivery, migration, and engraftment of stem cells to induce neuroprotection. L-myc expressing human neural stem cells (LMNSC008) demonstrate an inherent tropism to injury sites after intranasal (IN) administration. We hypothesize that IN delivered LMNSC008 cells migrate to primary and secondary injury sites and modulate biomarkers associated with neuroprotection and tissue regeneration. To test this hypothesis, immunocompetent adult female rats received either controlled cortical impact injury or sham surgery. LMNSC008 cells or a vehicle were administered IN on postoperative days 7, 9, 11, 13, 15, and 17. The distribution and migration of eGFP-expressing LMNSC008 cells were quantified over 1 mm-thick optically cleared (CLARITY) coronal brain sections from TBI and SHAM controls. NSC migration was observed along white matter tracts projecting toward the hippocampus and regions of TBI. ELISA and Nanostring assays revealed a shift in tissue gene expression in LMNSC008 treated rats relative to controls. LMNSC008 treatment reduced expression of genes and pathways involved in inflammatory response, microglial function, and various cytokines and receptors. Our proof-of-concept studies, although preliminary, support the rationale of using intranasal delivery of LMNSC008 cells for functional studies in preclinical models of TBI and provide support for potential translatability in TBI patients.

Model discovery approach enables non-invasive measurement of intra-tumoral fluid transport in dynamic MRI.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is a routine method to non-invasively quantify perfusion dynamics in tissues. The standard practice for analyzing DCE-MRI data is to fit an ordinary differential equation to each voxel. Recent advances in data science provide an opportunity to move beyond existing methods to obtain more accurate measurements of fluid properties. Here, we developed a localized convolutional function regression that enables simultaneous measurement of interstitial fluid velocity, diffusion, and perfusion in 3D. We validated the method computationally and experimentally, demonstrating accurate measurement of fluid dynamics in situ and in vivo. Applying the method to human MRIs, we observed tissue-specific differences in fluid dynamics, with an increased fluid velocity in breast cancer as compared to brain cancer. Overall, our method represents an improved strategy for studying interstitial flows and interstitial transport in tumors and patients. We expect that it will contribute to the better understanding of cancer progression and therapeutic response.

Neuroprotective potential of intranasally delivered L-myc immortalized human neural stem cells in female rats after a controlled cortical impact injury.

Efficacious stem cell-based therapies for traumatic brain injury (TBI) depend on successful delivery, migration, and engraftment of stem cells to induce neuroprotection. L-myc expressing human neural stem cells (LMNSC008) demonstrate an inherent tropism to injury sites after intranasal (IN) administration. We hypothesize that IN delivered LMNSC008 cells migrate to primary and secondary injury sites and modulate biomarkers associated with neuroprotection and tissue regeneration. To test this, immunocompetent adult female rats received a controlled cortical impact injury (CCI) or sham surgery. LMNSC008 cells or a vehicle (VEH) were administered IN on postoperative days 7, 9, 11, 13, 15, and 17. The distribution and migration of eGFP-expressing LMNSC008 cells were quantified over 1 mm-thick optically cleared (CLARITY) coronal brain sections from TBI and SHAM controls. NSC migration was observed along white matter tracts projecting toward the hippocampus and regions of TBI. ELISA and Nanostring assays revealed a shift in tissue gene expression in LMNSC008 treated rats relative to controls. LMNSC008 treatment reduced expression of genes and pathways involved in inflammatory response, microglial function, and various cytokines and receptors. The data demonstrate a robust proof-of-concept for LMNSC008 therapy for TBI and provides a strong rationale for IN delivery for translation in TBI patients.

Proteomics and mathematical modeling of longitudinal CSF differentiates fast versus slow ALS progression.

OBJECTIVE: Amyotrophic lateral sclerosis (ALS) is a heterogeneous disease with a complex etiology that lacks biomarkers predicting disease progression. The objective of this study was to use longitudinal cerebrospinal fluid (CSF) samples to identify biomarkers that distinguish fast progression (FP) from slow progression (SP) and assess their temporal response. METHODS: We utilized mass spectrometry (MS)-based proteomics to identify candidate biomarkers using longitudinal CSF from a discovery cohort of SP and FP ALS patients. Immunoassays were used to quantify and validate levels of the top biomarkers. A state-transition mathematical model was created using the longitudinal MS data that also predicted FP versus SP. RESULTS: We identified a total of 1148 proteins in the CSF of all ALS patients. Pathway analysis determined enrichment of pathways related to complement and coagulation cascades in FPs and synaptogenesis and glucose metabolism in SPs. Longitudinal analysis revealed a panel of 59 candidate markers that could segregate FP and SP ALS. Based on multivariate analysis, we identified three biomarkers (F12, RBP4, and SERPINA4) as top candidates that segregate ALS based on rate of disease progression. These proteins were validated in the discovery and a separate validation cohort. Our state-transition model determined that the overall variance of the proteome over time was predictive of the disease progression rate. INTERPRETATION: We identified pathways and protein biomarkers that distinguish rate of ALS disease progression. A mathematical model of the CSF proteome determined that the change in entropy of the proteome over time was predictive of FP versus SP.

Differential Distribution of Brain Metastases from Non-Small Cell Lung Cancer Based on Mutation Status.

Non-small cell lung cancer (NSCLC) has a high rate of brain metastasis. The purpose of this study was to assess the differential distribution of brain metastases from primary NSCLC based on mutation status. Brain MRI scans of patients with brain metastases from primary NSCLC were retrospectively analyzed. Brain metastatic tumors were grouped according to mutation status of their primary NSCLC and the neuroimaging features of these brain metastases were analyzed. A total of 110 patients with 1386 brain metastases from primary NSCLC were included in this study. Gray matter density at the tumor center peaked at ~0.6 for all mutations. The median depths of tumors were 7.9 mm, 8.7 mm and 9.1 mm for EGFR, ALK and KRAS mutation groups, respectively (p = 0.044). Brain metastases for the EGFR mutation-positive group were more frequently located in the left cerebellum, left cuneus, left precuneus and right precentral gyrus. In the ALK mutation-positive group, brain metastases were more frequently located in the right middle occipital gyrus, right posterior cingulate, right precuneus, right precentral gyrus and right parietal lobe. In the KRAS mutation-positive patient group, brain metastases were more frequently located in the posterior left cerebellum. Our study showed differential spatial distribution of brain metastases in patients with NSCLC according to their mutation status. Information regarding distribution of brain metastases is clinically relevant as it could be helpful to guide treatment planning for targeted therapy, and for predicting prognosis.

Data driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables.

In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.

Modeling interaction of Glioma cells and CAR T-cells considering multiple CAR T-cells bindings.

Chimeric antigen receptor (CAR) T-cell based immunotherapy has shown its potential in treating blood cancers, and its application to solid tumors is currently being extensively investigated. For glioma brain tumors, various CAR T-cell targets include IL13Rα2, EGFRvIII, HER2, EphA2, GD2, B7-H3, and chlorotoxin. In this work, we are interested in developing a mathematical model of IL13Rα2 targeting CAR T-cells for treating glioma. We focus on extending the work of Kuznetsov et al. (1994) by considering binding of multiple CAR T-cells to a single glioma cell, and the dynamics of these multi-cellular conjugates. Our model more accurately describes experimentally observed CAR T-cell killing assay data than the models which do not consider multi-cellular conjugates. Moreover, we derive conditions in the CAR T-cell expansion rate that determines treatment success or failure. Finally, we show that our model captures distinct CAR T-cell killing dynamics from low to high antigen receptor densities in patient-derived brain tumor cells.

Bow-tie architectures in biological and artificial neural networks: Implications for network evolution and assay design.

Modern artificial neural networks (ANNs) have long been designed on foundations of mathematics as opposed to their original foundations of biomimicry. However, the structure and function of these modern ANNs are often analogous to real-life biological networks. We propose that the ubiquitous information-theoretic principles underlying the development of ANNs are similar to the principles guiding the macro-evolution of biological networks and that insights gained from one field can be applied to the other. We generate hypotheses on the bow-tie network structure of the Janus kinase - signal transducers and activators of transcription (JAK-STAT) pathway, additionally informed by the evolutionary considerations, and carry out ANN simulation experiments to demonstrate that an increase in the network's input and output complexity does not necessarily require a more complex intermediate layer. This observation should guide novel biomarker discovery-namely, to prioritize sections of the biological networks in which information is most compressed as opposed to biomarkers representing the periphery of the network.

Structural and practical identifiability of contrast transport models for DCE-MRI.

Compartment models are widely used to quantify blood flow and transport in dynamic contrast-enhanced magnetic resonance imaging. These models analyze the time course of the contrast agent concentration, providing diagnostic and prognostic value for many biological systems. Thus, ensuring accuracy and repeatability of the model parameter estimation is a fundamental concern. In this work, we analyze the structural and practical identifiability of a class of nested compartment models pervasively used in analysis of MRI data. We combine artificial and real data to study the role of noise in model parameter estimation. We observe that although all the models are structurally identifiable, practical identifiability strongly depends on the data characteristics. We analyze the impact of increasing data noise on parameter identifiability and show how the latter can be recovered with increased data quality. To complete the analysis, we show that the results do not depend on specific tissue characteristics or the type of enhancement patterns of contrast agent signal.

Comparison of cell state models derived from single-cell RNA sequencing data: graph versus multi-dimensional space.

Single-cell sequencing technologies have revolutionized molecular and cellular biology and stimulated the development of computational tools to analyze the data generated from these technology platforms. However, despite the recent explosion of computational analysis tools, relatively few mathematical models have been developed to utilize these data. Here we compare and contrast two cell state geometries for building mathematical models of cell state-transitions with single-cell RNA-sequencing data with hematopoeisis as a model system; (i) by using partial differential equations on a graph representing intermediate cell states between known cell types, and (ii) by using the equations on a multi-dimensional continuous cell state-space. As an application of our approach, we demonstrate how the calibrated models may be used to mathematically perturb normal hematopoeisis to simulate, predict, and study the emergence of novel cell states during the pathogenesis of acute myeloid leukemia. We particularly focus on comparing the strength and weakness of the graph model and multi-dimensional model.