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The clinical practice of oncology is being transformed by molecular diagnostics that will enable predictive and personalized medicine. Current technologies for quantitation of the cancer proteome are either qualitative (e.g., immunohistochemistry) or require large sample sizes (e.g., flow cytometry). Here, we report a microfluidic platform, Microfluidic Image Cytometry (MIC), capable of quantitative, single-cell proteomic analysis of multiple signaling molecules using only 1,000-2,800 cells. Using cultured cell lines, we demonstrate simultaneous measurement of four critical signaling proteins (EGFR, PTEN, phospho-Akt and phospho-S6) within the oncogenic PI3K/Akt/mTOR signaling pathway. To demonstrate the clinical application of the MIC platform to solid tumors, we analyzed a panel of 19 human brain tumor biopsies, including glioblastomas. Our MIC measurements were validated by clinical immunohistochemistry and confirmed the striking inter- and intra-tumoral heterogeneity characteristic of glioblastoma. To interpret the multiparameter, single-cell MIC measurements, we adapted bioinformatic methods including self-organizing maps that stratify patients into clusters which predict tumor progression and patient survival. Together with bioinformatic analysis, the MIC platform represents a robust, enabling in vitro molecular diagnostic technology for systems pathology analysis and personalized medicine.
Technologies for the molecular diagnosis of cancer are rapidly changing the clinical practice of oncology (1, 2). As knowledge about the molecular basis of cancer increases, the development of tools capable of multiple, inexpensive biomarker measurements on small amounts of clinical tissue will be essential for the success of clinical trials, both to permit stratification of patients into groups most likely to benefit from targeted therapeutics and to evaluate the efficacy of such drugs on their molecular target.
For solid tumors, standard diagnostic methods rely on qualitative tissue immunohistochemistry (IHC) (3). Unfortunately, a wide range of variables limit quantification of IHC data (4), and multiparametric analyses via IHC are technologically challenging and rarely used clinically. Thus, histological analysis provides only limited insight into the molecular classification of tumors (5). In contrast, flow cytometry permits quantitative measurement of multiple proteins in individual cells (6), but high sample/reagent consumption generally limits diagnostic use to hematological cancers (7). Therefore, the molecular diagnosis of solid tumors necessitates a miniaturized platform featuring specimen economy and sensitive multiparametric measurement capabilities.
Glioblastoma multiforme (GBM) is the most lethal form of adult brain cancer and exhibits extensive molecular inter- and intra-tumoral heterogeneity (8). The PI3K/Akt/mTOR signaling pathway is frequently deregulated in GBM (8), often by overexpression of the epidermal growth factor receptor (EGFR) or other receptor tyrosine kinases (9, 10) and/or loss of the PTEN tumor suppressor (10, 11), leading to activation of the downstream effectors Akt and mTOR. The promise of targeted PI3K pathway inhibitors has led to some clinical improvement in patients (12), but therapeutic efficacy has been limited to a relatively small cohort of GBM patients (13, 14). Future development of successful targeted therapeutics for heterogeneous solid tumors like GBM will require the ability to detect molecular subsets that can guide appropriate patient selection in clinical trials (15).
Microfluidics exhibits intrinsic advantages of minimal sample/reagent usage, operational fidelity, high throughput, cost efficiency and precise control over reagent and sample delivery to microscale environments (16). These microscale technology platforms are finding application in biological assays including stem cell culture (17), gene expression (18), chromosomal analysis (19), and proteomics (20-23). Microfluidic platforms capable of single-cell analysis are also evolving, including a recent platform that allows single-cell interrogation of signaling networks in cultured cell lines (24). Given the clinical need for improved in vitro molecular diagnostic technologies that can characterize heterogeneity at the single cell level in primary brain tumor biopsies, we combined the advantages of microfluidics (16) and microscopy-based cytometry (25) to develop the Microfluidic Image Cytometry (MIC) platform.
Here, we utilize the MIC platform to demonstrate simultaneous, single-cell quantification of four signaling proteins (EGFR, PTEN, phospho-Akt and phospho-S6) within the PI3K/Akt/mTOR signaling pathway. We demonstrate clinical application of the MIC technology by analyzing a panel of 19 human brain tumor biopsies (including both GBMs and low-grade brain tumors) and validate our MIC measurements with clinical IHC protocols. To compare the single-cell multiparameter MIC data sets with clinical outcome measures, we adapt bioinformatic methods including self-organizing maps (SOMs) (26) to stratify tumor specimens into clusters and found that these clusters correlate with tumor progression and patient survival. Therefore, the MIC platform represents a novel in vitro molecular diagnostic technology that will enable systems pathology analysis of solid tumors and patient stratification for personalized medicine.
The cell array chip consists of 24 (3 × 8) cell culture chambers, each with dimensions of 8 mm (l) × 1 mm (w) × 120 μm (h) for a total volume of 960 nL. The cell array chip was fabricated by direct attachment of a polydimethylsiloxane (PDMS)-based microfluidic component onto a commercial poly-L-lysine (PLL)-coated glass slide (Polysciences) using an adhesive PDMS layer (Supplementary Fig. S1). The PDMS-based microfluidic component was fabricated by soft lithography methods using a silicon wafer replicate of photolithographically-defined microchannel patterns. Cells, culture media, and reagents were introduced into the cell array chips by an electronic, handheld pipette (Thermo Fisher Scientific).
The human glioblastoma cell line U87 was purchased from American Type Culture Collection. All U87 cell lines (27) (U87-PTEN, U87-EGFR, U87-PTEN-EGFR) were routinely maintained in DMEM containing 10% FBS and 1% penicillin/streptomycin (Invitrogen). Erlotinib was purchased from LC Laboratories and rapamycin and human recombinant EGF were from Sigma. For loading into microfluidic channels, U87 cells were dissociated using TrypLE (Invitrogen), pelleted and resuspended at a density of 250-500 cells/μL, and 2 μL of U87 cell suspension was loaded into each microfluidic channel (Supplementary Fig. S2). Chips were then placed in a 10 cm petri dish with 1 mL ddH2O and incubated in a 5% CO2, 37 °C incubator for 16 h prior to drug treatment and on-chip ICC. Cells were treated with 20 μM erlotinib for 48 h, 20 nM rapamycin for 48 h or 10 ng/ml EGF for 30 min.
All patients were consented with approved UCLA Institutional Review Board protocols. Patient tumors were brought directly from neurosurgery suites of Ronald Reagan UCLA Medical Center upon resection and placed on ice for rapid portioning by the attending neuropathologist (WHY). Tumor portions were washed in PBS, minced with a scalpel blade and dissociated into single-cell suspensions by TrypLE enzymatic digestion and gentle trituration, followed by a Percoll purification to remove cellular debris and red blood cells (28) (Supplementary Methods). Tumor cells were filtered through a 40 μm single cell strainer (Becton Dickson) and loaded at a density of approximately 100-1000 cells/μL into PLL-coated chips and centrifuged to facilitate cell attachment. Chips were then placed in a 10 cm petri dish with 1 mL ddH2O and placed in 5% CO2, 37 °C incubator for 15 min to allow cell attachment prior to on-chip ICC.
On-chip ICC involved cell fixation (4% paraformaldehyde for 15 min at RT), washing with PBS, cell permeabilization (0.3% Triton X-100 for 15 minutes at RT), washing, blocking (10% normal goat serum, 3% BSA and 0.1% N-doceyl-B-maltodextrose for 12 h at 4°C), immunolabeling (12 h at 4°C) followed by washing and DAPI staining prior to microscopy-based image cytometry. For immunolabeling, an optimized mixture of fluorophore-conjugated antibodies was prepared by mixing anti-EGFR (BD Pharmingen) labeled with LiCor/HiLyte Fluor 750 (Dojindo Molecular Technologies), PE-conjugated anti-PTEN (BD Biosciences), Alexa Fluor 647-conjugated anti-pS473-AKT (Cell Signaling Technology) and Alexa Fluor 488-conjugated anti-pS235/S236-S6 (Cell Signaling Technology).
Following image acquisition, MetaMorph (Molecular Devices, Version 220.127.116.11) was used to quantify fluorescent signals in individual cells using the Multi-Wavelength Cell Scoring module. Fluorescent intensity values were normalized by the cell-spread-surface-area and background staining was subtracted (Supplementary Methods). Data were logarithmically transformed to create Gaussian-like distributions for subsequent analysis.
IHC was carried out as previously described (27). Briefly, formalin-fixed, paraffin-embedded tissue samples were sectioned, stained with a PTEN monoclonal antibody (clone 6H2.1, DAKO), and counterstained with Mayer’s Hematoxylin. PTEN staining was analyzed and scored according to established methods (14). .
To analyze the single-cell multiparameter MIC measurements, self-organizing maps (SOMs) were created in R using the Kohonen package of Wehrens & Buydens (29). Briefly, a SOM grid consists of a set of units characterized by a vector of four values (EGFR, PTEN, pAkt and pS6), and MIC measurements are mapped to the SOM grid based on similarity to the characteristics of the SOM units. The vectors characterizing the SOM grid were trained using an input data set representing the global measurement space (Supplementary Methods). After training, each tumor specimen was individually mapped to the SOM grid and plotted as the frequency of cells mapping to each SOM unit. To cluster the SOM mappings of the tumor specimens, we calculated a neighborhood frequency (the sum of the frequencies for a SOM unit and its neighbors, Supplementary Fig. S12A), and these values were subjected to unsupervised hierarchical clustering using the average-linkage method based on the Pearson correlation (30). Data were visualized using Java Treeview (31).
Overall survival was determined as the interval between the date of surgery where the tumor specimen was obtained for MIC analysis and last date of known clinical follow-up or date of death using death certificates and the social security death index. Time to progression was determined by the duration of progression-free survival from the date of surgery until recurrence, death, or, if progression-free, until the last follow-up date. Overall survival and time-to-progression were related to the SOM-derived clusters using a Cox proportional hazards model (Stata 8.0) (32). This analysis was performed in the full patient cohort comparing the patients belonging to each SOM-derived cluster against the remaining patients. All p-values were two-tailed and p < 0.05 was considered significant. Survival distributions were presented as Kaplan-Meier plots.
To develop a molecular diagnostic tool for multiparameter pathology analysis of solid tumor specimens, we designed a simple monolithic microfluidic device to enable quantitative immunocytochemistry (ICC). The microfluidic image cytometry (MIC) platform integrates (i) a polydimethylsiloxane (PDMS)-based microfluidic cell array chip for accommodating up to 24 cellular samples and performing ICC (Fig. 1A) with (ii) fluorescence microscopy and imaging software for quantitative cytometry, followed by multiparameter pathology analysis (Fig. 1B). Chip fabrication utilizes soft lithography techniques, followed by direct attachment of the PDMS chip onto a poly-L-lysine-coated glass slide using an adhesive PDMS film (Materials and Methods and Supplementary Fig. S1). Automated pipetting enables parallel cell culture and quantitative ICC on approximately 1,000 to 2,800 cells per sample (Supplementary Fig. S2), making the MIC platform ideal for highly efficient parallel measurement of up to 24 samples of less than 3,000 cells.
Before testing the MIC platform on primary patient samples, we optimized ICC and microscopy-based cytometry protocols using the U87 GBM cell line and variants overexpressing EGFR, PTEN, or EGFR with PTEN (U87-EGFR, U87-PTEN, U87-PTEN-EGFR, respectively (33)) to demonstrate reproducible quantification of EGFR, PTEN, pAKT and pS6 expression/phosphorylation levels. Although some GBMs often overexpress a constitutively-active mutant form of EGFR (EGFRvIII), we utilized an antibody that recognizes EGFR but not EGFRvIII (J.S. and H.R.T., unpublished observation) because intratumoral expression of wild-type EGFR is typically more extensive than this mutant form (34). On-chip growth curves (confirmed that the microfluidic environment did not affect proliferation rates compared to off-chip cell culture Supplementary Fig. S3). ICC and image processing protocols were developed by: i) optimization of antibody concentrations and confirmation of minimal cross-reactivity among antibodies (35) (Supplementary Fig. S4); ii) standardization of microscopy parameters (i.e., exposure, light source, gain) (Supplementary Methods); and iii) demonstration of measurement reproducibility (Supplementary Fig. S5). These data demonstrate that the optimized MIC protocols allow reproducible, simultaneous, single-cell measurement of EGFR, PTEN, pAkt and pS6 in cultured cell lines.
Prior to application of the MIC platform to analysis of primary patient samples, we established the dynamic range of MIC measurement for EGFR, PTEN, pAKT and pS6. Using U87 cell lines expressing EGFR and/or PTEN, the MIC platform demonstrated at least an order of magnitude signal separation between positive and negative controls for all four signaling proteins (Fig. 2A). Because microfluidics should offer highly reduced sample requirements compared to traditional methods, we also evaluated specimen economy and found that traditional Western blotting requires 2-3 orders of magnitude more cells than MIC analysis in order to yield similar results (Supplementary Fig. S6). To assess the sensitivity of MIC measurements, we used Pten wild-type and Pten knockout MEF cell lines (36) and verified that MIC can detect differences in endogenous PTEN expression (Supplementary Fig. S7). Therefore, MIC offers a highly sensitive platform for simultaneous single-cell quantification of the PI3K/Akt/mTOR pathway with microscopic sample sizes.
Because solid tumors like GBM exhibit significant intratumoral heterogeneity (8), we next tested the ability of the MIC platform to resolve heterogeneous populations of cancer cells by analyzing a mixture of U87 isogenic cell lines overexpressing EGFR and/or PTEN using the MIC platform. Qualitative examination of the four-color overlay image revealed the expected differences in protein expression within the cell mixture (Fig. 2B). Quantitative analysis of this U87 cell mixture using a 2D contour plot revealed four clusters clearly identifying the four U87 cell lines (Fig. 2C). These results were confirmed by a similar analysis of the four individually-stained cell lines (Supplementary Fig. S8), thus demonstrating that the MIC platform can quantitatively discriminate distinct molecularly-defined subsets within a heterogeneous cell mixture.
Having demonstrated that the MIC platform can quantitatively characterize heterogeneous mixtures of cultured cells, we next tested the utility of the MIC for clinical molecular diagnostics of human tumor tissue. To allow for analysis of solid tumors, we adapted an established tissue processing protocol for dissociation of tumor cells into a single-cell suspension and optimized critical aspects of sample preparation to ensure reproducibility (Supplementary Information) (28). With this protocol, we then analyzed a cohort of 19 clinical brain tumor specimens including GBMs and several low-grade tumor types including oligoastrocytomas and oligodendriomas (Supplementary Table S1). Notably, MIC analysis required only 1,000-2,800 cells, far fewer than would have been necessary for analysis by population average techniques such as Western blotting. We verified that MIC measurements did not correlate with either the total number of cells measured or the number of cells per MIC channel (data not shown). Using rank-based graphs of MIC measurements from a subset of tumors, we first demonstrated extensive intra- and inter-tumoral heterogeneity in single-cell expression levels of EGFR, PTEN, pAkt and pS6 (Fig. 3A and Supplementary Fig. S9). These data show that the MIC platform can quantitatively capture the molecular heterogeneity characteristic of GBM and other brain tumor types (8).
Since PTEN expression is routinely measured by IHC in the clinic, we compared our MIC measurements to clinically-practiced IHC protocols (14) (Fig. 3B and Supplementary Table S1). Although the quantitative single-cell MIC data is fundamentally different than qualitative IHC scoring, we found that the percentage of cells expressing PTEN as scored by IHC corroborated the MIC measurements for 8 of 9 cases. The discrepancy between clinical IHC and MIC measurements of PTEN expression in Patient 7 may be due to the extremely heterogeneous nature of this sample, where evidence of foamy macrophages, necrosis and normal brain were found. Thus, clinical IHC validated the accuracy of our quantitative, single-cell MIC measurements.
Meaningful interpretation of the multiparameter single-cell MIC measurements from resected brain tumors requires the application of bioinformatic techniques. To facilitate systems pathology analysis of these human brain tumor specimens, we adapted SOMs (26), an unsupervised learning method which has found wide application in analysis of complex biological data sets (37-39). SOMs project high-dimensional data onto a 2D grid where the topological location of points represents similarity or dissimilarity (Supplementary Fig. S10), thus placing highly similar multidimensional objects in close proximity to each other on the SOM grid (29). When applied to MIC measurements, each SOM unit represents a characteristic set of EGFR, PTEN, pAkt and pS6 expression levels (Fig. 4A). For each patient sample, a color scale indicates the frequency of cells that map to the SOM units, and the resulting pattern provides a visual summary of the similarities, dissimilarities and the degree of heterogeneity within a set of multiparameter, single-cell MIC measurements.
Examining SOM mappings for all 19 clinical brain tumor specimens, we again observed striking inter- and intra-tumoral heterogeneity (Fig. 4B), as previously shown using single-parameter measurements (Fig. 3A and Supplementary Fig. S9). In addition, we found that the degree of intra-tumoral heterogeneity could be quantitatively assessed by varying the size of the SOM grid (Supplementary Fig. S11), with homogeneous tumors (e.g., Patients 1, 3 and 14) and heterogeneous tumors (e.g., Patients 8, 11 and 12) exhibiting concentrated and dispersed SOM mappings, respectively. To test the possibility of using MIC-derived SOMs for patient stratification, we represented each SOM mapping as a neighborhood frequency vector (NFV, the sum of the frequency of cells mapped to a SOM unit and its surrounding neighbors, Fig. 5A and Supplementary Fig. S12A) and performed unsupervised clustering of the 19 patient-specific NFVs. Clustering of these NFVs revealed three predominant clusters of patient samples (Fig. 5B and Supplemental Fig. S12). Although Cluster II was comprised only of GBMs, both Clusters I and III exhibited mixed tumor type composition. We deconvoluted the original staining patterns that characterize each cluster to reveal expression/signaling phenotypes and found that Cluster I (8 patient samples) exhibits medium EGFR, low PTEN and high pS6 expression. Cluster II (4 patient samples) exhibits high expression of EGFR, PTEN and pAkt, and Cluster III (7 patient samples) exhibits low EGFR and pS6 expression. By ANOVA analysis, EGFR was the most discriminatory biomarker between the three clusters, followed in decreasing order by pS6, PTEN and pAkt (Fig. 5B and Supplemental Fig. 12D). Thus, SOMs can serve as a technique for stratification of multiparameter, single-cell MIC measurements of clinical brain tumor specimens.
To assess the clinical significance of these groupings, we tested whether these MIC-derived clusters correlated with clinical outcome measures. Although the median duration between tumor resection and survival analysis was shorter (317 days) than the median survival time of GBM patients (~ 365 days (8)), we found that Cluster II was significantly associated with an increased hazard of patient death (hazard ratio [HR] > 5.35, p < 0.05) (Fig. 5C and Supplementary Fig. S13). Conversely, Cluster I was significantly associated with a decreased hazard of patient death (HR < 0.001, p < 0.001), and Cluster III did not exhibit any significant difference in overall survival. Analysis of progression-free survival demonstrated similar trends to overall survival, although the hazard ratios were not statistically different from the remaining cohort (Supplementary Fig. S13). This analysis demonstrates the potential of the MIC platform for classification of molecularly-defined patient subsets of clinical significance.
The clinical diagnosis of cancer is being transformed from phenomenological descriptions to molecular, systems-based disease models. Quantitative, sensitive and inexpensive single-cell molecular diagnostic measurements of precious clinical samples will both increase our knowledge of the etiology of cancer and enable the development and judicious application of targeted therapeutics (1, 2). Here, we report a new technology, Microfluidic Image Cytometry (MIC), which combines the advantages of microfluidics and microscope-based cytometry to enable multiparameter pathology analysis of solid tumors. The design, application and analysis of the MIC systems pathology platform represents a novel synthesis of several technological developments, including i) microfluidic ‘chip’ design to enable inexpensive, robust, multiparameter, single-cell quantitation of precious samples, ii) improved processing and handling of sensitive tumor samples and iii) adaptation of bioinformatic methods to interpret high-dimensional data. Because of the demonstrated clinical need for molecular classification of gliomas (13, 14), we targeted the oncogenic PI3K/Akt/mTOR pathway in brain tumors of varying stages and pathological states, including GBM.
Microfluidics has emerged as a promising platform for molecular diagnosis of clinical samples (2, 16), with demonstrated applications including the detection of chromosomal translocations (19), measurement of oncoprotein expression and phosphorylation (20), and biomarker measurements in serum and saliva (21, 40). While integrated microfluidic devices have previously been used to dissect two-parameter dynamics of signal transduction in cultured cell lines (24), we have expanded the utility of microfluidic platforms to four-parameter in vitro molecular diagnosis using microscopic amounts of human clinical tissue. The MIC platform specifically addresses shortcomings of currently-practiced clinical diagnostics, including the qualitative imprecision of IHC (3) and the high sample/reagent consumption requirements of flow cytometry (7).
The single-cell nature of these MIC measurements permitted novel characterization of inter- and intra-tumoral heterogeneity in solid tumors. As expected from an infamously heterogeneous tumor type like GBM, we observed a diversity of signaling phenotypes that would have been masked by population-average measurements (Figs. (Figs.3A3A and and4B).4B). Although IHC-based analyses of tissue microarrays have enabled systems analysis of glioblastomas (27), these techniques offer only semi-quantitative measurement of successive tissue slices, as opposed to simultaneous, single-cell quantification of multiple biomarkers. Much as flow cytometry has enabled single-cell phospho-proteomics in liquid and some solid tumors to identify cancer cell subsets that predict clinical outcome (41), we expect that further application of the MIC to solid tumors will reveal molecular signatures that are unmeasurable by population-average techniques (42).
The ability to discriminate and characterize molecular subsets within and between patients will be essential for efficacious use of effective targeted therapeutics in highly heterogeneous solid tumors like glioma (15), particularly given that one molecularly-targeted drug, the EGFR kinase inhibitor erlotinib, proved effective only in a subset of patients expressing both the constitutively-active EGFRvIII mutant and PTEN (14). Here, we have demonstrated that bioinformatic analysis of MIC measurements can reveal molecular signatures that predict tumor progression and patient survival (Fig. 5C). Notably, Cluster II exhibits an increased hazard of patient death, potentially because of high EGFR expression since EGFR is the most discriminatory biomarker between the clusters (Supplemental Fig. 12D) and high EGFR expression is negatively correlated with GBM patient survival outcome (43). Importantly, univariate survival analysis did not reveal significant correlation between any of the individual EGFR/PI3K/Akt/mTOR pathway components and patient survival, demonstrating the improved performance of the multiparameter signature approach. However, given the relatively small size of our patient cohort (19 patients), these SOM-based signatures will require validation in a larger, independent data set prior to full comparison to other established biomarker trends (44). Finally, although none of the patients included in this study were treated with targeted inhibitors against the PI3K/Akt/mTOR pathway (e.g., erlotinib, rapamycin, see Supplemental Table 1), future studies will be designed to identify links between the SOM-based stratification of patients described here and previously identified molecular signatures predictive of a positive response to targeted inhibitors (14).
Given the relatively short median duration between tumor resection and outcome analysis (317 days), we note that long-term follow-up studies on larger patient cohorts will be required to validate the clinical significance of MIC-derived, SOM-based molecular signatures. Nevertheless, the encouraging prognostic significance in a relatively small sample size demonstrates the potential of integrating bioinformatic analysis with single-cell measurements to stratify solid tumor biopsies into clusters with clinical relevance. Future studies utilizing the MIC platform will expand the number of measured biomarkers using additional fluorophores and quantum dots (45), in expectation that additional measured biomarkers will enable a more thorough systems analysis and permit further dissection of molecular subtypes and identification of biomarker signatures in GBM (e.g., PDGFR, IDH1, NF1, Notch) (46, 47). As the number of measured biomarkers expands, the need for bioinformatic analysis techniques such as SOMs will become even greater.
In summary, we have developed MIC (Microfluidic Image Cytometry), a highly precise, reliable technology platform requiring microscopic amounts of reagents (~2 μL/channel) and samples (≤ 3,000 cells) for multiparamater, quantitative single-cell systems pathology of solid tumors. Because of the assay’s flexible nature, we envision rapid application both to comparison of molecular endpoints pre- and post-treatment in clinical samples using fine-needle biopsies (48) and to analysis of in vitro prognostic models such as multipassage neurosphere cultures (49). Coupled with systems pathology analysis, the MIC technology platform represents one of the first emerging microtechnologies to provide meaningful correlations between measurements of minute patient samples and clinical prognosis. As such, the MIC platform represents a novel technology for quantitative multiparameter pathology to enable prospective studies integrating in vitro molecular diagnostics, systems analysis of disease, and patient stratification for personalized medicine (2, 5).
DOE, NSBCC, UCLA Brain Tumor Translational Resource, H.I.K was supported by NIH NINDS NS052563, N.A.G. is a postdoctoral trainee supported by the UCLA Tumor Biology Program USHHS Ruth L. Kirschstein Institutional National Research Service Award # T32 CA009056. T.G.G. is an Alfred P. Sloan Research Fellow.