Simulating tumor volume dynamics in response to radiotherapy: Implications of model selection.

From the beginning of the usage of radiotherapy (RT) for cancer treatment, mathematical modeling has been integral to understanding radiobiology and for designing treatment approaches and schedules. There has been extensive modeling of response to RT with the inclusion of various degrees of biological complexity. In this study, we compare three models of tumor volume dynamics: (1) exponential growth with RT directly reducing tumor volume, (2) logistic growth with direct tumor volume reduction, and (3) logistic growth with RT reducing the tumor carrying capacity with the objective of understanding the implications of model selection and informing the process of model calibration and parameterization. For all three models, we: examined the rates of change in tumor volume during and RT treatment course; performed parameter sensitivity and identifiability analyses; and investigated the impact of the parameter sensitivity on the tumor volume trajectories. In examining the tumor volume dynamics trends, we coined a new metric - the point of maximum reduction of tumor volume (MRV) - to quantify the magnitude and timing of the expected largest impact of RT during a treatment course. We found distinct timing differences in MRV, dependent on model selection. The parameter identifiability and sensitivity analyses revealed the interdependence of the different model parameters and that it is only possible to independently identify tumor growth and radiation response parameters if the underlying tumor growth rate is sufficiently large. Ultimately, the results of these analyses help us to better understand the implications of model selection while simultaneously generating falsifiable hypotheses about MRV timing that can be tested on longitudinal measurements of tumor volume from pre-clinical or clinical data with high acquisition frequency. Although, our study only compares three particular models, the results demonstrate that caution is necessary in selecting models of response to RT, given the artifacts imposed by each model.

Mathematical modeling of radiotherapy: impact of model selection on estimating minimum radiation dose for tumor control.

Introduction: Radiation therapy (RT) is one of the most common anticancer therapies. Yet, current radiation oncology practice does not adapt RT dose for individual patients, despite wide interpatient variability in radiosensitivity and accompanying treatment response. We have previously shown that mechanistic mathematical modeling of tumor volume dynamics can simulate volumetric response to RT for individual patients and estimation personalized RT dose for optimal tumor volume reduction. However, understanding the implications of the choice of the underlying RT response model is critical when calculating personalized RT dose. Methods: In this study, we evaluate the mathematical implications and biological effects of 2 models of RT response on dose personalization: (1) cytotoxicity to cancer cells that lead to direct tumor volume reduction (DVR) and (2) radiation responses to the tumor microenvironment that lead to tumor carrying capacity reduction (CCR) and subsequent tumor shrinkage. Tumor growth was simulated as logistic growth with pre-treatment dynamics being described in the proliferation saturation index (PSI). The effect of RT was simulated according to each respective model for a standard schedule of fractionated RT with 2 Gy weekday fractions. Parameter sweeps were evaluated for the intrinsic tumor growth rate and the radiosensitivity parameter for both models to observe the qualitative impact of each model parameter. We then calculated the minimum RT dose required for locoregional tumor control (LRC) across all combinations of the full range of radiosensitvity and proliferation saturation values. Results: Both models estimate that patients with higher radiosensitivity will require a lower RT dose to achieve LRC. However, the two models make opposite estimates on the impact of PSI on the minimum RT dose for LRC: the DVR model estimates that tumors with higher PSI values will require a higher RT dose to achieve LRC, while the CCR model estimates that higher PSI values will require a lower RT dose to achieve LRC. Discussion: Ultimately, these results show the importance of understanding which model best describes tumor growth and treatment response in a particular setting, before using any such model to make estimates for personalized treatment recommendations.

Rethinking the immunotherapy numbers game.

Immunotherapies are a major breakthrough in oncology, yielding unprecedented response rates for some cancers. Especially in combination with conventional treatments or targeted agents, immunotherapeutics offer invaluable tools to improve outcomes for many patients. However, why not all patients have a favorable response remains unclear. There is an increasing appreciation of the contributions of the complex tumor microenvironment, and the tumor-immune ecosystem in particular, to treatment outcome. To date, however, there exists no immune biomarker to explain why two patients with similar clinical stage and molecular profile would have different treatment outcomes. We hypothesize that it is critical to understand both the immune and tumor states to understand how the complex system will respond to treatment. Here, we present how integrated mathematical oncology approaches can help conceptualize the effect of various immunotherapies on a patient's tumor and local immune environment, and how combinations of immunotherapy and cytotoxic therapy may be used to improve tumor response and control and limit toxicity on a per patient basis.

Structural Design of Multidentate Copolymers as Compact Quantum Dot Coatings for Live-Cell Single-Particle Imaging.

Quantum dots (QDs) are a class of semiconductor nanocrystal used broadly as fluorescent emitters for analytical studies in the life sciences. These nanomaterials are particularly valuable for single-particle imaging and tracking applications in cells and tissues. An ongoing technological goal is to reduce the hydrodynamic size of QDs to enhance access to sterically hindered biological targets. Multidentate polymer coatings are a focus of these efforts and have resulted in compact and stable QDs with hydrodynamic diameters near 10 nm. New developments are needed to reach smaller sizes to further enhance transport through pores in cells and tissues. Here, we describe how structural characteristics of linear multidentate copolymers determine hydrodynamic size, colloidal stability, and biomolecular interactions of coated QDs. We tune copolymer composition, degree of polymerization, and hydrophilic group length, and coat polymers on CdSe and (core)shell (HgCdSe)CdZnS QDs. We find that a broad range of polymer structures and compositions yield stable colloidal dispersions; however, hydrodynamic size minimization and nonspecific binding resistance can only be simultaneously achieved within a narrow range of properties, requiring short polymers, balanced compositions, and small nanocrystals. In quantitative single-molecule imaging assays in synapses of live neurons, size reduction progressively increases labeling specificity of neurotransmitter receptors. Our findings provide a design roadmap to next-generation QDs with sizes approaching fluorescent protein labels that are the standard of many live-cell biomolecular studies.

Dynamics-Adapted Radiotherapy Dose (DARD) for Head and Neck Cancer Radiotherapy Dose Personalization.

Standard of care radiotherapy (RT) doses have been developed as a one-size-fits all approach designed to maximize tumor control rates across a population. Although this has led to high control rates for head and neck cancer with 66-70 Gy, this is done without considering patient heterogeneity. We present a framework to estimate a personalized RT dose for individual patients, based on pre- and early on-treatment tumor volume dynamics-a dynamics-adapted radiotherapy dose (DDARD). We also present the results of an in silico trial of this dose personalization using retrospective data from a combined cohort of n = 39 head and neck cancer patients from the Moffitt and MD Anderson Cancer Centers that received 66-70 Gy RT in 2-2.12 Gy weekday fractions. This trial was repeated constraining DDARD between (54, 82) Gy to test more moderate dose adjustment. DDARD was estimated to range from 8 to 186 Gy, and our in silico trial estimated that 77% of patients treated with standard of care were overdosed by an average dose of 39 Gy, and 23% underdosed by an average dose of 32 Gy. The in silico trial with constrained dose adjustment estimated that locoregional control could be improved by >10%. We demonstrated the feasibility of using early treatment tumor volume dynamics to inform dose personalization and stratification for dose escalation and de-escalation. These results demonstrate the potential to both de-escalate most patients, while still improving population-level control rates.

Forecasting Individual Patient Response to Radiation Therapy in Head and Neck Cancer With a Dynamic Carrying Capacity Model.

PURPOSE: To model and predict individual patient responses to radiation therapy. METHODS AND MATERIALS: We modeled tumor dynamics as logistic growth and the effect of radiation as a reduction in the tumor carrying capacity, motivated by the effect of radiation on the tumor microenvironment. The model was assessed on weekly tumor volume data collected for 2 independent cohorts of patients with head and neck cancer from the H. Lee Moffitt Cancer Center (MCC) and the MD Anderson Cancer Center (MDACC) who received 66 to 70 Gy in standard daily fractions or with accelerated fractionation. To predict response to radiation therapy for individual patients, we developed a new forecasting framework that combined the learned tumor growth rate and carrying capacity reduction fraction (δ) distribution with weekly measurements of tumor volume reduction for a given test patient to estimate δ, which was used to predict patient-specific outcomes. RESULTS: The model fit data from MCC with high accuracy with patient-specific δ and a fixed tumor growth rate across all patients. The model fit data from an independent cohort from MDACC with comparable accuracy using the tumor growth rate learned from the MCC cohort, showing transferability of the growth rate. The forecasting framework predicted patient-specific outcomes with 76% sensitivity and 83% specificity for locoregional control and 68% sensitivity and 85% specificity for disease-free survival with the inclusion of 4 on-treatment tumor volume measurements. CONCLUSIONS: These results demonstrate that our simple mathematical model can describe a variety of tumor volume dynamics. Furthermore, combining historically observed patient responses with a few patient-specific tumor volume measurements allowed for the accurate prediction of patient outcomes, which may inform treatment adaptation and personalization.

Optimizing Quantum Dot Probe Size for Single-Receptor Imaging.

Quantum dots (QDs) are nanocrystals with bright fluorescence and long-term photostability, attributes particularly beneficial for single-molecule imaging and molecular counting in the life sciences. The size of a QD nanocrystal determines its physicochemical and photophysical properties, both of which dictate the success of imaging applications. Larger nanocrystals typically have better optical properties, with higher brightness, red-shifted emission, reduced blinking, and greater stability. However, larger nanocrystals introduce molecular-labeling biases due to steric hindrance and nonspecific binding. Here, we systematically analyze the impact of nanocrystal size on receptor labeling in live and fixed cells. We designed three (core)shell QDs with red emission (600-700 nm) and crystalline sizes of 3.2, 5.5, and 8.3 nm. After coating with the same multidentate polymer, hydrodynamic sizes were 9.2 nm (QD9.2), 13.3 nm (QD13.3), and 17.4 nm (QD17.4), respectively. The QDs were conjugated to streptavidin and applied as probes for biotinylated neurotransmitter receptors. QD9.2 exhibited the highest labeling specificity for receptors in the narrow synaptic cleft (∼20-30 nm) in living neurons. However, for dense receptor labeling for molecular counting in live and fixed HeLa cells, QD13.3 yielded the highest counts. Nonspecific binding rose sharply for hydrodynamic sizes larger than 13.3 nm, with QD17.4 exhibiting particularly diminished specificity. Our comparisons further highlight needs to continue engineering the smallest QDs to increase single-molecule intensity, suppress blinking frequency, and inhibit nonspecific labeling in fixed and permeabilized cells. These results lay a foundation for designing QD probes with further reduced sizes to achieve unbiased labeling for quantitative and single-molecule imaging.

Short-Wave Infrared Quantum Dots with Compact Sizes as Molecular Probes for Fluorescence Microscopy.

Materials with short-wave infrared (SWIR) emission are promising contrast agents for in vivo animal imaging, providing high-contrast and high-resolution images of blood vessels in deep tissues. However, SWIR emitters have not been developed as molecular labels for microscopy applications in the life sciences, which require optimized probes that are bright, stable, and small. Here, we design and synthesize semiconductor quantum dots (QDs) with SWIR emission based on HgxCd1-xSe alloy cores red shifted to the SWIR by epitaxial deposition of thin HgxCd1-xS shells with a small band gap. By tuning alloy composition alone, the emission can be shifted across the visible-to-SWIR (VIR) spectra while maintaining a small and equal size, allowing direct comparisons of molecular labeling performance across a broad range of wavelength. After coating with click-functional multidentate polymers, the VIR-QD spectral series has high quantum yield in the SWIR (14-33%), compact size (13 nm hydrodynamic diameter), and long-term stability in aqueous media during continuous excitation. We show that these properties enable diverse applications of SWIR molecular probes for fluorescence microscopy using conjugates of antibodies, growth factors, and nucleic acids. A broadly useful outcome is a 10-55-fold enhancement of the signal-to-background ratio at both the single-molecule level and the ensemble level in the SWIR relative to visible wavelengths, primarily due to drastically reduced autofluorescence. We anticipate that VIR-QDs with SWIR emission will enable ultrasensitive molecular imaging of low-copy number analytes in biospecimens with high autofluorescence.

High-Fidelity Single Molecule Quantification in a Flow Cytometer Using Multiparametric Optical Analysis.

Microfluidic techniques are widely used for high-throughput quantification and discrete analysis of micron-scale objects but are difficult to apply to molecular-scale targets. Instead, single-molecule methods primarily rely on low-throughput microscopic imaging of immobilized molecules. Here we report that commercial-grade flow cytometers can detect single nucleic acid targets following enzymatic extension and dense labeling with multiple distinct fluorophores. We focus on microRNAs, short nucleic acids that can be extended by rolling circle amplification (RCA). We labeled RCA-extended microRNAs with multicolor fluorophores to generate repetitive nucleic acid products with submicron sizes and tunable multispectral profiles. By cross-correlating the multiparametric optical features, signal-to-background ratios were amplified 1600-fold to allow single-molecule detection across 4 orders of magnitude of concentration. The limit of detection was measured to be 47 fM, which is 100-fold better than gold-standard methods based on polymerase chain reaction. Furthermore, multiparametric analysis allowed discrimination of different microRNA sequences in the same solution using distinguishable optical barcodes. Barcodes can apply both ratiometric and colorimetric signatures, which could facilitate high-dimensional multiplexing. Because of the wide availability of flow cytometers, we anticipate that this technology can provide immediate access to high-throughput multiparametric single-molecule measurements and can further be adapted to the diverse range of molecular amplification methods that are continually emerging.

Single quantum dot tracking reveals the impact of nanoparticle surface on intracellular state.

Inefficient delivery of macromolecules and nanoparticles to intracellular targets is a major bottleneck in drug delivery, genetic engineering, and molecular imaging. Here we apply live-cell single-quantum-dot imaging and tracking to analyze and classify nanoparticle states after intracellular delivery. By merging trajectory diffusion parameters with brightness measurements, multidimensional analysis reveals distinct and heterogeneous populations that are indistinguishable using single parameters alone. We derive new quantitative metrics of particle loading, cluster distribution, and vesicular release in single cells, and evaluate intracellular nanoparticles with diverse surfaces following osmotic delivery. Surface properties have a major impact on cell uptake, but little impact on the absolute cytoplasmic numbers. A key outcome is that stable zwitterionic surfaces yield uniform cytosolic behavior, ideal for imaging agents. We anticipate that this combination of quantum dots and single-particle tracking can be widely applied to design and optimize next-generation imaging probes, nanoparticle therapeutics, and biologics.

Multidentate Polymer Coatings for Compact and Homogeneous Quantum Dots with Efficient Bioconjugation.

Quantum dots are fluorescent nanoparticles used to detect and image proteins and nucleic acids. Compared with organic dyes and fluorescent proteins, these nanocrystals have enhanced brightness, photostability, and wavelength tunability, but their larger size limits their use. Recently, multidentate polymer coatings have yielded stable quantum dots with small hydrodynamic dimensions (≤10 nm) due to high-affinity, compact wrapping around the nanocrystal. However, this coating technology has not been widely adopted because the resulting particles are frequently heterogeneous and clustered, and conjugation to biological molecules is difficult to control. In this article we develop new polymeric ligands and optimize coating and bioconjugation methodologies for core/shell CdSe/Cd(x)Zn(1-x)S quantum dots to generate homogeneous and compact products. We demonstrate that "ligand stripping" to rapidly displace nonpolar ligands with hydroxide ions allows homogeneous assembly with multidentate polymers at high temperature. The resulting aqueous nanocrystals are 7-12 nm in hydrodynamic diameter, have quantum yields similar to those in organic solvents, and strongly resist nonspecific interactions due to short oligoethylene glycol surfaces. Compared with a host of other methods, this technique is superior for eliminating small aggregates identified through chromatographic and single-molecule analysis. We also demonstrate high-efficiency bioconjugation through azide-alkyne click chemistry and self-assembly with hexa-histidine-tagged proteins that eliminate the need for product purification. The conjugates retain specificity of the attached biomolecules and are exceptional probes for immunofluorescence and single-molecule dynamic imaging. These results are expected to enable broad utilization of compact, biofunctional quantum dots for studying crowded macromolecular environments such as the neuronal synapse and cellular cytoplasm.

Lipoprotein Nanoplatelets: Brightly Fluorescent, Zwitterionic Probes with Rapid Cellular Entry.

Semiconductor nanoplatelets (NPLs) are planar nanocrystals that have recently attracted considerable attention due to their quantum-well-like physics, atomically precise thickness, and unique photophysical properties such as narrow-band fluorescence emission. These attributes are of potential interest for applications in biomolecular and cellular imaging, but it has been challenging to colloidally stabilize these nanocrystals in biological media due to their large dimensions and tendency to aggregate. Here we introduce a new colloidal material that is a hybrid between a NPL and an organic nanodisc composed of phospholipids and lipoproteins. The phospholipids adsorb to flat surfaces on the NPL, and lipoproteins bind to sharp edges to enable monodisperse NPL encapsulation with long-term stability in biological buffers and high-salt solutions. The lipoprotein NPLs (L-NPLs) are highly fluorescent, with brightness comparable to that of wavelength-matched quantum dots at both the ensemble and single-molecule levels. They also exhibit a unique feature of rapid internalization into living cells, after which they retain their fluorescence. These unique properties suggest that L-NPLs are particularly well suited for applications in live-cell single-molecule imaging and multiplexed cellular labeling.

Brightness-equalized quantum dots.

As molecular labels for cells and tissues, fluorescent probes have shaped our understanding of biological structures and processes. However, their capacity for quantitative analysis is limited because photon emission rates from multicolour fluorophores are dissimilar, unstable and often unpredictable, which obscures correlations between measured fluorescence and molecular concentration. Here we introduce a new class of light-emitting quantum dots with tunable and equalized fluorescence brightness across a broad range of colours. The key feature is independent tunability of emission wavelength, extinction coefficient and quantum yield through distinct structural domains in the nanocrystal. Precise tuning eliminates a 100-fold red-to-green brightness mismatch of size-tuned quantum dots at the ensemble and single-particle levels, which substantially improves quantitative imaging accuracy in biological tissue. We anticipate that these materials engineering principles will vastly expand the optical engineering landscape of fluorescent probes, facilitate quantitative multicolour imaging in living tissue and improve colour tuning in light-emitting devices.