Comparing mechanism-based and machine learning models for predicting the effects of glucose accessibility on tumor cell proliferation.

Glucose plays a central role in tumor metabolism and development and is a target for novel therapeutics. To characterize the response of cancer cells to blockade of glucose uptake, we collected time-resolved microscopy data to track the growth of MDA-MB-231 breast cancer cells. We then developed a mechanism-based, mathematical model to predict how a glucose transporter (GLUT1) inhibitor (Cytochalasin B) influences the growth of the MDA-MB-231 cells by limiting access to glucose. The model includes a parameter describing dose dependent inhibition to quantify both the total glucose level in the system and the glucose level accessible to the tumor cells. Four common machine learning models were also used to predict tumor cell growth. Both the mechanism-based and machine learning models were trained and validated, and the prediction error was evaluated by the coefficient of determination (R2). The random forest model provided the highest accuracy predicting cell dynamics (R2 = 0.92), followed by the decision tree (R2 = 0.89), k-nearest-neighbor regression (R2 = 0.84), mechanism-based (R2 = 0.77), and linear regression model (R2 = 0.69). Thus, the mechanism-based model has a predictive capability comparable to machine learning models with the added benefit of elucidating biological mechanisms.

A data assimilation framework to predict the response of glioma cells to radiation.

We incorporate a practical data assimilation methodology into our previously established experimental-computational framework to predict the heterogeneous response of glioma cells receiving fractionated radiation treatment. Replicates of 9L and C6 glioma cells grown in 96-well plates were irradiated with six different fractionation schemes and imaged via time-resolved microscopy to yield 360- and 286-time courses for the 9L and C6 lines, respectively. These data were used to calibrate a biology-based mathematical model and then make predictions within two different scenarios. For Scenario 1, 70% of the time courses are fit to the model and the resulting parameter values are averaged. These average values, along with the initial cell number, initialize the model to predict the temporal evolution for each test time course (10% of the data). In Scenario 2, the predictions for the test cases are made with model parameters initially assigned from the training data, but then updated with new measurements every 24 hours via four versions of a data assimilation framework. We then compare the predictions made from Scenario 1 and the best version of Scenario 2 to the experimentally measured microscopy measurements using the concordance correlation coefficient (CCC). Across all fractionation schemes, Scenario 1 achieved a CCC value (mean ± standard deviation) of 0.845 ± 0.185 and 0.726 ± 0.195 for the 9L and C6 cell lines, respectively. For the best data assimilation version from Scenario 2 (validated with the last 20% of the data), the CCC values significantly increased to 0.954 ± 0.056 (p = 0.002) and 0.901 ± 0.061 (p = 8.9e-5) for the 9L and C6 cell lines, respectively. Thus, we have developed a data assimilation approach that incorporates an experimental-computational system to accurately predict the in vitro response of glioma cells to fractionated radiation therapy.

A Case Series Exploration of Multi-Regional Expression Heterogeneity in Triple-Negative Breast Cancer Patients.

Extensive intratumoral heterogeneity (ITH) is believed to contribute to therapeutic failure and tumor recurrence, as treatment-resistant cell clones can survive and expand. However, little is known about ITH in triple-negative breast cancer (TNBC) because of the limited number of single-cell sequencing studies on TNBC. In this study, we explored ITH in TNBC by evaluating gene expression-derived and imaging-derived multi-region differences within the same tumor. We obtained tissue specimens from 10 TNBC patients and conducted RNA sequencing analysis of 2-4 regions per tumor. We developed a novel analysis framework to dissect and characterize different types of variability: between-patients (inter-tumoral heterogeneity), between-patients across regions (inter-tumoral and region heterogeneity), and within-patient, between-regions (regional intratumoral heterogeneity). We performed a Bayesian changepoint analysis to assess and classify regional variability as low (convergent) versus high (divergent) within each patient feature (TNBC and PAM50 subtypes, immune, stroma, tumor counts and tumor infiltrating lymphocytes). Gene expression signatures were categorized into three types of variability: between-patients (108 genes), between-patients across regions (183 genes), and within-patients, between-regions (778 genes). Based on the between-patient gene signature, we identified two distinct patient clusters that differed in menopausal status. Significant intratumoral divergence was observed for PAM50 classification, tumor cell counts, and tumor-infiltrating T cell abundance. Other features examined showed a representation of both divergent and convergent results. Lymph node stage was significantly associated with divergent tumors. Our results show extensive intertumoral heterogeneity and regional ITH in gene expression and image-derived features in TNBC. Our findings also raise concerns regarding gene expression based TNBC subtyping. Future studies are warranted to elucidate the role of regional heterogeneity in TNBC as a driver of treatment resistance.

A Multi-Compartment Model of Glioma Response to Fractionated Radiation Therapy Parameterized via Time-Resolved Microscopy Data.

PURPOSE: Conventional radiobiology models, including the linear-quadratic model, do not explicitly account for the temporal effects of radiation, thereby making it difficult to make time-resolved predictions of tumor response to fractionated radiation. To overcome this limitation, we propose and validate an experimental-computational approach that predicts the changes in cell number over time in response to fractionated radiation. METHODS: We irradiated 9L and C6 glioma cells with six different fractionation schemes yielding a total dose of either 16 Gy or 20 Gy, and then observed their response via time-resolved microscopy. Phase-contrast images and Cytotox Red images (to label dead cells) were collected every 4 to 6 hours up to 330 hours post-radiation. Using 75% of the total data (i.e., 262 9L curves and 211 C6 curves), we calibrated a two-species model describing proliferative and senescent cells. We then applied the calibrated parameters to a validation dataset (the remaining 25% of the data, i.e., 91 9L curves and 74 C6 curves) to predict radiation response. Model predictions were compared to the microscopy measurements using the Pearson correlation coefficient (PCC) and the concordance correlation coefficient (CCC). RESULTS: For the 9L cells, we observed PCCs and CCCs between the model predictions and validation data of (mean ± standard error) 0.96 ± 0.007 and 0.88 ± 0.013, respectively, across all fractionation schemes. For the C6 cells, we observed PCCs and CCCs between model predictions and the validation data were 0.89 ± 0.008 and 0.75 ± 0.017, respectively, across all fractionation schemes. CONCLUSION: By proposing a time-resolved mathematical model of fractionated radiation response that can be experimentally verified in vitro, this study is the first to establish a framework for quantitative characterization and prediction of the dynamic radiobiological response of 9L and C6 gliomas to fractionated radiotherapy.

Generative adversarial network enables rapid and robust fluorescence lifetime image analysis in live cells.

Fluorescence lifetime imaging microscopy (FLIM) is a powerful tool to quantify molecular compositions and study molecular states in complex cellular environment as the lifetime readings are not biased by fluorophore concentration or excitation power. However, the current methods to generate FLIM images are either computationally intensive or unreliable when the number of photons acquired at each pixel is low. Here we introduce a new deep learning-based method termed flimGANE (fluorescence lifetime imaging based on Generative Adversarial Network Estimation) that can rapidly generate accurate and high-quality FLIM images even in the photon-starved conditions. We demonstrated our model is up to 2,800 times faster than the gold standard time-domain maximum likelihood estimation (TD_MLE) and that flimGANE provides a more accurate analysis of low-photon-count histograms in barcode identification, cellular structure visualization, Förster resonance energy transfer characterization, and metabolic state analysis in live cells. With its advantages in speed and reliability, flimGANE is particularly useful in fundamental biological research and clinical applications, where high-speed analysis is critical.

Longitudinal FRET Imaging of Glucose and Lactate Dynamics and Response to Therapy in Breast Cancer Cells.

PURPOSE: The reprogramming of cellular metabolism is a hallmark of cancer. The ability to noninvasively assay glucose and lactate concentrations in cancer cells would improve our understanding of the dynamic changes in metabolic activity accompanying tumor initiation, progression, and response to therapy. Unfortunately, common approaches for measuring these nutrient levels are invasive or interrupt cell growth. This study transfected FRET reporters quantifying glucose and lactate concentration into breast cancer cell lines to study nutrient dynamics and response to therapy. PROCEDURES: Two FRET reporters, one assaying glucose concentration and one assaying lactate concentration, were stably transfected into the MDA-MB-231 breast cancer cell line. Correlation between FRET measurements and ligand concentration were measured using a confocal microscope and a cell imaging plate reader. Longitudinal changes in glucose and lactate concentration were measured in response to treatment with CoCl2, cytochalasin B, and phloretin which, respectively, induce hypoxia, block glucose uptake, and block glucose and lactate transport. RESULTS: The FRET ratio from the glucose and lactate reporters increased with increasing concentration of the corresponding ligand (p < 0.005 and p < 0.05, respectively). The FRET ratio from both reporters was found to decrease over time for high initial concentrations of the ligand (p < 0.01). Significant differences in the FRET ratio corresponding to metabolic inhibition were found when cells were treated with glucose/lactate transporter inhibitors. CONCLUSIONS: FRET reporters can track intracellular glucose and lactate dynamics in cancer cells, providing insight into tumor metabolism and response to therapy over time.

Bayesian calibration of a stochastic, multiscale agent-based model for predicting in vitro tumor growth.

Hybrid multiscale agent-based models (ABMs) are unique in their ability to simulate individual cell interactions and microenvironmental dynamics. Unfortunately, the high computational cost of modeling individual cells, the inherent stochasticity of cell dynamics, and numerous model parameters are fundamental limitations of applying such models to predict tumor dynamics. To overcome these challenges, we have developed a coarse-grained two-scale ABM (cgABM) with a reduced parameter space that allows for an accurate and efficient calibration using a set of time-resolved microscopy measurements of cancer cells grown with different initial conditions. The multiscale model consists of a reaction-diffusion type model capturing the spatio-temporal evolution of glucose and growth factors in the tumor microenvironment (at tissue scale), coupled with a lattice-free ABM to simulate individual cell dynamics (at cellular scale). The experimental data consists of BT474 human breast carcinoma cells initialized with different glucose concentrations and tumor cell confluences. The confluence of live and dead cells was measured every three hours over four days. Given this model, we perform a time-dependent global sensitivity analysis to identify the relative importance of the model parameters. The subsequent cgABM is calibrated within a Bayesian framework to the experimental data to estimate model parameters, which are then used to predict the temporal evolution of the living and dead cell populations. To this end, a moment-based Bayesian inference is proposed to account for the stochasticity of the cgABM while quantifying uncertainties due to limited temporal observational data. The cgABM reduces the computational time of ABM simulations by 93% to 97% while staying within a 3% difference in prediction compared to ABM. Additionally, the cgABM can reliably predict the temporal evolution of breast cancer cells observed by the microscopy data with an average error and standard deviation for live and dead cells being 7.61±2.01 and 5.78±1.13, respectively.

An experimental-mathematical approach to predict tumor cell growth as a function of glucose availability in breast cancer cell lines.

We present the development and validation of a mathematical model that predicts how glucose dynamics influence metabolism and therefore tumor cell growth. Glucose, the starting material for glycolysis, has a fundamental influence on tumor cell growth. We employed time-resolved microscopy to track the temporal change of the number of live and dead tumor cells under different initial glucose concentrations and seeding densities. We then constructed a family of mathematical models (where cell death was accounted for differently in each member of the family) to describe overall tumor cell growth in response to the initial glucose and confluence conditions. The Akaikie Information Criteria was then employed to identify the most parsimonious model. The selected model was then trained on 75% of the data to calibrate the system and identify trends in model parameters as a function of initial glucose concentration and confluence. The calibrated parameters were applied to the remaining 25% of the data to predict the temporal dynamics given the known initial glucose concentration and confluence, and tested against the corresponding experimental measurements. With the selected model, we achieved an accuracy (defined as the fraction of measured data that fell within the 95% confidence intervals of the predicted growth curves) of 77.2 ± 6.3% and 87.2 ± 5.1% for live BT-474 and MDA-MB-231 cells, respectively.

A time-resolved experimental-mathematical model for predicting the response of glioma cells to single-dose radiation therapy.

PURPOSE: To develop and validate a mechanism-based, mathematical model that characterizes 9L and C6 glioma cells' temporal response to single-dose radiation therapy in vitro by explicitly incorporating time-dependent biological interactions with radiation. METHODS: We employed time-resolved microscopy to track the confluence of 9L and C6 glioma cells receiving radiation doses of 0, 2, 4, 6, 8, 10, 12, 14 or 16 Gy. DNA repair kinetics are measured by γH2AX expression via flow cytometry. The microscopy data (814 replicates for 9L, 540 replicates for C6 at various seeding densities receiving doses above) were divided into training (75%) and validation (25%) sets. A mechanistic model was developed, and model parameters were calibrated to the training data. The model was then used to predict the temporal dynamics of the validation set given the known initial confluences and doses. The predictions were compared to the corresponding dynamic microscopy data. RESULTS: For 9L, we obtained an average (± standard deviation, SD) Pearson correlation coefficient between the predicted and measured confluence of 0.87 ± 0.16, and an average (±SD) concordance correlation coefficient of 0.72 ± 0.28. For C6, we obtained an average (±SD) Pearson correlation coefficient of 0.90 ± 0.17, and an average (±SD) concordance correlation coefficient of 0.71 ± 0.24. CONCLUSION: The proposed model can effectively predict the temporal development of 9L and C6 glioma cells in response to a range of single-fraction radiation doses. By developing a mechanism-based, mathematical model that can be populated with time-resolved data, we provide an experimental-mathematical framework that allows for quantitative investigation of cells' temporal response to radiation. Our approach provides two key advances: (i) a time-resolved, dynamic death rate with a clear biological interpretation, and (ii) accurate predictions over a wide range of cell seeding densities and radiation doses.

Effects of magnetic fields on intracellular calcium oscillations.

Based on the model of the two calcium stores developed by Goldbeter, and the viewpoint that the cell membrane is a major site of interaction for extremely-low-frequency (ELF) electromagnetic fields, the permeability of ions can be changed by electromagnetic fields, a theoretical model of cytosolic calcium oscillations influenced by magnetic fields is presented. It is shown that, the field frequency condition will influence the pattern of calcium oscillation while the field strength was given, and the magnetic field strength will change the pattern of calcium oscillation when the frequency was 50Hz and 100Hz. Therefore, intracellular calcium oscillations can be influenced by ELF magnetic fields and then a series cellular response could be transformed.