@article{nguyen_rutter_flores_2023, title={Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data}, volume={85}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-023-01162-3}, abstractNote={Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models' performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions.}, number={7}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Nguyen, Kyle and Rutter, Erica M. and Flores, Kevin B.}, year={2023}, month={Jul} }
 @article{warrier_rutter_flores_2022, title={Multitask neural networks for predicting bladder pressure with time series data}, volume={72}, ISSN={["1746-8108"]}, DOI={10.1016/j.bspc.2021.103298}, abstractNote={Multitask learning (MTL) can improve accuracy over vanilla neural networks in modeling population level time series data. This can be accomplished by assigning the prediction for each individual in the population as a separate task, thereby leveraging the heterogeneity of population level data. Here, we investigate a novel approach by training recurrent neural networks (RNNs) in a multitask setting. We apply this new methodology to experimental data for predicting bladder pressure, and then bladder contractions, from an external urethral sphincter electromyograph (EUS EMG) signal. We found that the multitask models make more accurate individual level predictions than their single tasking counterparts. We observed that, for bladder pressure prediction, either incorporating multitask learning or RNN structure generalized best to out of sample test data and multitasking RNNs had high out of sample correlation coefficients. These results suggest that MTL models could be used to leverage heterogeneous population time series data for making individualized predictions. From these bladder pressure predictions, we predicted the onset of bladder contractions. Our results indicate that the MTL RNN model was superior in both intra- and inter-individual bladder contraction predictions as measured by sensitivity (85.7%), specificity (98.7%) and precision (73.5%).}, journal={BIOMEDICAL SIGNAL PROCESSING AND CONTROL}, author={Warrier, Sangeeta and Rutter, Erica M. and Flores, Kevin B.}, year={2022}, month={Feb} }
 @article{lagergren_flores_gilman_tsynkov_2021, title={Deep Learning Approach to the Detection of Scattering Delay in Radar Images}, volume={15}, ISSN={["1559-8616"]}, DOI={10.1007/s42519-020-00149-w}, number={1}, journal={JOURNAL OF STATISTICAL THEORY AND PRACTICE}, author={Lagergren, John and Flores, Kevin and Gilman, Mikhail and Tsynkov, Semyon}, year={2021}, month={Mar} }
 @article{zhang_flores_tran_2021, title={Deep learning and regression approaches to forecasting blood glucose levels for type 1 diabetes}, volume={69}, ISSN={["1746-8108"]}, DOI={10.1016/j.bspc.2021.102923}, abstractNote={Objective: Controlling blood glucose in the euglycemic range is the main goal of developing the closed-loop insulin delivery system for type 1 diabetes patients. The closed-loop system delivers the amount of insulin dose determined by glucose predictions through the use of computational algorithms. A computationally efficient and accurate model that can capture the physiological nonlinear dynamics is critical for developing an efficient closed-loop system. Methods: Four data-driven models are compared, including different neural network architectures, a reservoir computing model, and a novel linear regression approach. Model predictions are evaluated over continuous 30 and 60 min time horizons using real-world data from wearable sensor measurements, a continuous glucose monitor, and self-reported events through mobile applications. The four data-driven models are trained on 12 data contributors for around 32 days, 8 days of data are used for validation, with an additional 10 days of data for out-of-sample testing. Model performance was evaluated by the root mean squared error and the mean absolute error. Results: A neural network model using an encoder-decoder architecture has the most stable performance and is able to recover missing dynamics in short time intervals. Regression models performed better at long-time prediction horizons (i.e., 60 min) and with lower computational costs. Significance: The performance of several distinct models was tested for individual-level data from a type 1 diabetes data set. These results may enable a feasible solution with low computational cost for the time-dependent adjustment of artificial pancreas for diabetes patients.}, journal={BIOMEDICAL SIGNAL PROCESSING AND CONTROL}, author={Zhang, Meng and Flores, Kevin B. and Tran, Hien T.}, year={2021}, month={Aug} }
 @misc{nardini_baker_simpson_flores_2021, title={Learning differential equation models from stochastic agent-based model simulations}, volume={18}, ISSN={["1742-5662"]}, DOI={10.1098/rsif.2020.0987}, abstractNote={Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology and epidemiology. Analysis of the model dynamics can be challenging due to their inherent stochasticity and heavy computational requirements. Common approaches to the analysis of agent-based models include extensive Monte Carlo simulation of the model or the derivation of coarse-grained differential equation models to predict the expected or averaged output from the agent-based model. Both of these approaches have limitations, however, as extensive computation of complex agent-based models may be infeasible, and coarse-grained differential equation models can fail to accurately describe model dynamics in certain parameter regimes. We propose that methods from the equation learning field provide a promising, novel and unifying approach for agent-based model analysis. Equation learning is a recent field of research from data science that aims to infer differential equation models directly from data. We use this tutorial to review how methods from equation learning can be used to learn differential equation models from agent-based model simulations. We demonstrate that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so. We highlight these advantages through several case studies involving two agent-based models that are broadly applicable to biological phenomena: a birth-death-migration model commonly used to explore cell biology experiments and a susceptible-infected-recovered model of infectious disease spread.}, number={176}, journal={JOURNAL OF THE ROYAL SOCIETY INTERFACE}, author={Nardini, John T. and Baker, Ruth E. and Simpson, Matthew J. and Flores, Kevin B.}, year={2021}, month={Mar} }
 @article{mcdaniel_flores_akpa_2021, title={Predicting Inter-individual Variability During Lipid Resuscitation of Bupivacaine Cardiotoxicity in Rats: A Virtual Population Modeling Study}, volume={7}, ISSN={["1179-6901"]}, url={https://doi.org/10.1007/s40268-021-00353-4}, DOI={10.1007/s40268-021-00353-4}, abstractNote={Intravenous lipid emulsions (ILE) have been credited for successful resuscitation in drug intoxication cases where other cardiac life-support methods have failed. However, inter-individual variability can function as a confounder that challenges our ability to define the scope of efficacy for lipid interventions, particularly as relevant data are scarce. To address this challenge, we developed a quantitative systems pharmacology model to predict outcome variability and shed light on causal mechanisms in a virtual population of rats subjected to bupivacaine toxicity and ILE intervention.We combined a physiologically based pharmacokinetic-pharmacodynamic model with data from a small study in Sprague-Dawley rats to characterize individual-specific cardiac responses to lipid infusion. We used the resulting individual parameter estimates to posit a population distribution of responses to lipid infusion. On that basis, we constructed a large virtual population of rats (N = 10,000) undergoing lipid therapy following bupivacaine cardiotoxicity.Using unsupervised clustering to assign resuscitation endpoints, our simulations predicted that treatment with a 30% lipid emulsion increases bupivacaine median lethal dose (LD50) by 46% when compared with a simulated control fluid. Prior experimental findings indicated an LD50 increase of 48%. Causal analysis of the population data suggested that muscle accumulation rather than liver accumulation of bupivacaine drives survival outcomes.Our results represent a successful prediction of complex, dynamic physiological outcomes over a virtual population. Despite being informed by very limited data, our mechanistic model predicted a plausible range of treatment outcomes that accurately predicts changes in LD50 when extrapolated to putatively toxic doses of bupivacaine. Furthermore, causal analysis of the predicted survival outcomes indicated a critical synergy between scavenging and direct cardiotonic mechanisms of ILE action.}, journal={DRUGS IN R&D}, publisher={Springer Science and Business Media LLC}, author={McDaniel, Matthew and Flores, Kevin B. and Akpa, Belinda S.}, year={2021}, month={Jul} }
 @article{peace_frost_wagner_danger_accolla_antczak_brooks_costello_everett_flores_et al._2021, title={Stoichiometric Ecotoxicology for a Multisubstance World}, volume={71}, ISSN={["1525-3244"]}, DOI={10.1093/biosci/biaa160}, abstractNote={Abstract Nutritional and contaminant stressors influence organismal physiology, trophic interactions, community structure, and ecosystem-level processes; however, the interactions between toxicity and elemental imbalance in food resources have been examined in only a few ecotoxicity studies. Integrating well-developed ecological theories that cross all levels of biological organization can enhance our understanding of ecotoxicology. In the present article, we underline the opportunity to couple concepts and approaches used in the theory of ecological stoichiometry (ES) to ask ecotoxicological questions and introduce stoichiometric ecotoxicology, a subfield in ecology that examines how contaminant stress, nutrient supply, and elemental constraints interact throughout all levels of biological organization. This conceptual framework unifying ecotoxicology with ES offers potential for both empirical and theoretical studies to deepen our mechanistic understanding of the adverse outcomes of chemicals across ecological scales and improve the predictive powers of ecotoxicology.}, number={2}, journal={BIOSCIENCE}, author={Peace, Angela and Frost, Paul C. and Wagner, Nicole D. and Danger, Michael and Accolla, Chiara and Antczak, Philipp and Brooks, Bryan W. and Costello, David M. and Everett, Rebecca A. and Flores, Kevin B. and et al.}, year={2021}, month={Feb}, pages={132–147} }
 @article{nardini_stolz_flores_harrington_byrne_2021, title={Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis}, volume={17}, ISSN={["1553-7358"]}, DOI={10.1371/journal.pcbi.1009094}, abstractNote={Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.}, number={6}, journal={PLOS COMPUTATIONAL BIOLOGY}, author={Nardini, John T. and Stolz, Bernadette J. and Flores, Kevin B. and Harrington, Heather A. and Byrne, Helen M.}, year={2021}, month={Jun} }
 @misc{everett_flores_henscheid_lagergren_larripa_li_nardini_nguyen_pitman_rutter_2020, title={A tutorial review of mathematical techniques for quantifying tumor heterogeneity}, volume={17}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2020207}, abstractNote={<abstract> <![CDATA[Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at <a href="https://github.com/jtnardin/Tumor-Heterogeneity/" target="_blank">https://github.com/jtnardin/Tumor-Heterogeneity/</a> so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018–2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.]]> </abstract>}, number={4}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Everett, Rebecca and Flores, Kevin B. and Henscheid, Nick and Lagergren, John and Larripa, Kamila and Li, Ding and Nardini, John T. and Nguyen, Phuong T. T. and Pitman, E. Bruce and Rutter, Erica M.}, year={2020}, pages={3660–3709} }
 @article{lagergren_nardini_baker_simpson_flores_2020, title={Biologically-informed neural networks guide mechanistic modeling from sparse experimental data}, volume={16}, ISSN={["1553-7358"]}, DOI={10.1371/journal.pcbi.1008462}, abstractNote={Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities [2].}, number={12}, journal={PLOS COMPUTATIONAL BIOLOGY}, author={Lagergren, John H. and Nardini, John T. and Baker, Ruth E. and Simpson, Matthew J. and Flores, Kevin B.}, year={2020}, month={Dec} }
 @article{saberi-bosari_flores_san-miguel_2020, title={Deep learning-enabled analysis reveals distinct neuronal phenotypes induced by aging and cold-shock}, volume={18}, ISSN={["1741-7007"]}, url={http://dx.doi.org/10.1186/s12915-020-00861-w}, DOI={10.1186/s12915-020-00861-w}, abstractNote={Abstract Background Access to quantitative information is crucial to obtain a deeper understanding of biological systems. In addition to being low-throughput, traditional image-based analysis is mostly limited to error-prone qualitative or semi-quantitative assessment of phenotypes, particularly for complex subcellular morphologies. The PVD neuron in Caenorhabditis elegans , which is responsible for harsh touch and thermosensation, undergoes structural degeneration as nematodes age characterized by the appearance of dendritic protrusions. Analysis of these neurodegenerative patterns is labor-intensive and limited to qualitative assessment. Results In this work, we apply deep learning to perform quantitative image-based analysis of complex neurodegeneration patterns exhibited by the PVD neuron in C. elegans . We apply a convolutional neural network algorithm (Mask R-CNN) to identify neurodegenerative subcellular protrusions that appear after cold-shock or as a result of aging. A multiparametric phenotypic profile captures the unique morphological changes induced by each perturbation. We identify that acute cold-shock-induced neurodegeneration is reversible and depends on rearing temperature and, importantly, that aging and cold-shock induce distinct neuronal beading patterns. Conclusion The results of this work indicate that implementing deep learning for challenging image segmentation of PVD neurodegeneration enables quantitatively tracking subtle morphological changes in an unbiased manner. This analysis revealed that distinct patterns of morphological alteration are induced by aging and cold-shock, suggesting different mechanisms at play. This approach can be used to identify the molecular components involved in orchestrating neurodegeneration and to characterize the effect of other stressors on PVD degeneration.}, number={1}, journal={BMC BIOLOGY}, publisher={Springer Science and Business Media LLC}, author={Saberi-Bosari, Sahand and Flores, Kevin B. and San-Miguel, Adriana}, year={2020}, month={Sep} }
 @article{nardini_lagergren_hawkins-daarud_curtin_morris_rutter_swanson_flores_2020, title={Learning Equations from Biological Data with Limited Time Samples}, volume={82}, ISSN={["1522-9602"]}, DOI={10.1007/s11538-020-00794-z}, abstractNote={Equation learning methods present a promising tool to aid scientists in the modeling process for biological data. Previous equation learning studies have demonstrated that these methods can infer models from rich datasets; however, the performance of these methods in the presence of common challenges from biological data has not been thoroughly explored. We present an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data. The performance of this methodology is thoroughly investigated in the face of several common challenges presented by biological data, namely, sparse data sampling, large noise levels, and heterogeneity between datasets. We find that this methodology can accurately infer the correct underlying equation and predict unobserved system dynamics from a small number of time samples when the data are sampled over a time interval exhibiting both linear and nonlinear dynamics. Our findings suggest that equation learning methods can be used for model discovery and selection in many areas of biology when an informative dataset is used. We focus on glioblastoma multiforme modeling as a case study in this work to highlight how these results are informative for data-driven modeling-based tumor invasion predictions.}, number={9}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Nardini, John T. and Lagergren, John H. and Hawkins-Daarud, Andrea and Curtin, Lee and Morris, Bethan and Rutter, Erica M. and Swanson, Kristin R. and Flores, Kevin B.}, year={2020}, month={Sep} }
 @article{lagergren_nardini_michael lavigne_rutter_flores_2020, title={Learning partial differential equations for biological transport models from noisy spatio-temporal data}, volume={476}, ISSN={["1471-2946"]}, DOI={10.1098/rspa.2019.0800}, abstractNote={We investigate methods for learning partial differential equation (PDE) models from spatiotemporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select candidate terms from a denoised set of data, including approximated partial derivatives. We analyze the performance in utilizing previous methods to denoise data for the task of discovering the governing system of partial differential equations (PDEs). We also develop a novel methodology that uses artificial neural networks (ANNs) to denoise data and approximate partial derivatives. We test the methodology on three PDE models for biological transport, i.e., the advection-diffusion, classical Fisher-KPP, and nonlinear Fisher-KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.}, number={2234}, journal={PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES}, author={Lagergren, John H. and Nardini, John T. and Michael Lavigne, G. and Rutter, Erica M. and Flores, Kevin B.}, year={2020}, month={Feb} }
 @article{san miguel_ramirez_flores_2020, title={Lifelong Analysis of Key Aging Genes as Determinants of Lifespan in <it>C</it>. <it>elegans</it>}, volume={34}, ISSN={["1530-6860"]}, DOI={10.1096/fasebj.2020.34.s1.00160}, journal={FASEB JOURNAL}, author={San Miguel, Adriana and Ramirez, Javier and Flores, Kevin}, year={2020}, month={Apr} }
 @article{rutter_lagergren_flores_2018, title={Automated Object Tracing for Biomedical Image Segmentation Using a Deep Convolutional Neural Network}, volume={11073}, ISBN={["978-3-030-00936-6"]}, ISSN={["1611-3349"]}, DOI={10.1007/978-3-030-00937-3_78}, abstractNote={Convolutional neural networks (CNNs) have been used for fast and accurate segmentation of medical images. In this paper, we present a novel methodology that uses CNNs for segmentation by mimicking the human task of tracing object boundaries. The architecture takes as input a patch of an image with an overlay of previously traced pixels and the output predicts the coordinates of the next m pixels to be traced. We also consider a CNN architecture that leverages the output from another semantic segmentation CNN, e.g., U-net, as an auxiliary image channel. To initialize the trace path in an image, we use either locations identified as object boundaries with high confidence from a semantic segmentation CNN or a short manually traced path. By iterating the CNN output, our method continues the trace until it intersects with the beginning of the path. We show that our network is more accurate than the state-of-the-art semantic segmentation CNN on microscopy images from the ISBI cell tracking challenge. Moreover, our methodology provides a natural platform for performing human-in-the-loop segmentation that is more accurate than CNNs alone and orders of magnitude faster than manual segmentation.}, journal={MEDICAL IMAGE COMPUTING AND COMPUTER ASSISTED INTERVENTION - MICCAI 2018, PT IV}, author={Rutter, Erica M. and Lagergren, John H. and Flores, Kevin B.}, year={2018}, pages={686–694} }
 @article{rutter_langdale_hokanson_hamilton_tran_grill_flores_2018, title={Detection of Bladder Contractions From the Activity of the External Urethral Sphincter in Rats Using Sparse Regression}, volume={26}, ISSN={1534-4320 1558-0210}, url={http://dx.doi.org/10.1109/tnsre.2018.2854675}, DOI={10.1109/tnsre.2018.2854675}, abstractNote={Bladder overactivity and incontinence and dysfunction can be mitigated by electrical stimulation of the pudendal nerve applied at the onset of a bladder contraction. Thus, it is important to predict accurately both bladder pressure and the onset of bladder contractions. We propose a novel method for prediction of bladder pressure using a time-dependent spectrogram representation of external urethral sphincter electromyographic (EUS EMG) activity and a least absolute shrinkage and selection operator regression model. There was a statistically significant improvement in prediction of bladder pressure compared with methods based on the firing rate of EUS EMG activity. This approach enabled prediction of the onset of bladder contractions with 91% specificity and 96% sensitivity and may be suitable for closed-loop control of bladder continence.}, number={8}, journal={IEEE Transactions on Neural Systems and Rehabilitation Engineering}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={Rutter, Erica M. and Langdale, Christopher L. and Hokanson, James A. and Hamilton, Franz and Tran, Hien and Grill, Warren M. and Flores, Kevin B.}, year={2018}, month={Aug}, pages={1636–1644} }
 @article{rutter_banks_flores_2018, title={Estimating intratumoral heterogeneity from spatiotemporal data}, volume={77}, ISSN={["1432-1416"]}, DOI={10.1007/s00285-018-1238-6}, abstractNote={Glioblastoma multiforme (GBM) is a malignant brain cancer with a tendency to both migrate and proliferate. We propose modeling GBM with heterogeneity in cell phenotypes using a random differential equation version of the reaction–diffusion equation, where the parameters describing diffusion (D) and proliferation ( $$\rho $$ ) are random variables. We investigate the ability to perform the inverse problem to recover the probability distributions of D and $$\rho $$ using the Prohorov metric, for a variety of probability distribution functions. We test the ability to perform the inverse problem for noisy synthetic data. We then examine the predicted effect of treatment, specifically, chemotherapy, when assuming such a heterogeneous population and compare with predictions from a homogeneous cell population model.}, number={6-7}, journal={JOURNAL OF MATHEMATICAL BIOLOGY}, author={Rutter, E. M. and Banks, H. T. and Flores, K. B.}, year={2018}, month={Dec}, pages={1999–2022} }
 @article{lagergren_reeder_hamilton_smith_flores_2018, title={Forecasting and Uncertainty Quantification Using a Hybrid of Mechanistic and Non-mechanistic Models for an Age-Structured Population Model}, volume={80}, ISSN={0092-8240 1522-9602}, url={http://dx.doi.org/10.1007/s11538-018-0421-7}, DOI={10.1007/s11538-018-0421-7}, abstractNote={In this paper, we present a new method for the prediction and uncertainty quantification of data-driven multivariate systems. Traditionally, either mechanistic or non-mechanistic modeling methodologies have been used for prediction; however, it is uncommon for the two to be incorporated together. We compare the forecast accuracy of mechanistic modeling, using Bayesian inference, a non-mechanistic modeling approach based on state space reconstruction, and a novel hybrid methodology composed of the two for an age-structured population data set. The data come from cannibalistic flour beetles, in which it is observed that the adults preying on the eggs and pupae result in non-equilibrium population dynamics. Uncertainty quantification methods for the hybrid models are outlined and illustrated for these data. We perform an analysis of the results from Bayesian inference for the mechanistic model and hybrid models to suggest reasons why hybrid modeling methodology may enable more accurate forecasts of multivariate systems than traditional approaches.}, number={6}, journal={Bulletin of Mathematical Biology}, publisher={Springer Nature}, author={Lagergren, John and Reeder, Amanda and Hamilton, Franz and Smith, Ralph C. and Flores, Kevin B.}, year={2018}, month={Apr}, pages={1578–1595} }
 @article{rutter_banks_leblanc_flores_2017, title={Continuous Structured Population Models for Daphnia magna}, volume={79}, ISSN={0092-8240 1522-9602}, url={http://dx.doi.org/10.1007/s11538-017-0344-8}, DOI={10.1007/s11538-017-0344-8}, abstractNote={We continue our efforts in modeling Daphnia magna, a species of water flea, by proposing a continuously structured population model incorporating density-dependent and density-independent fecundity and mortality rates. We collected new individual-level data to parameterize the individual demographics relating food availability and individual daphnid growth. Our model is fit to experimental data using the generalized least-squares framework, and we use cross-validation and Akaike Information Criteria to select hyper-parameters. We present our confidence intervals on parameter estimates.}, number={11}, journal={Bulletin of Mathematical Biology}, publisher={Springer Nature}, author={Rutter, Erica M. and Banks, H. T. and LeBlanc, Gerald A. and Flores, Kevin B.}, year={2017}, month={Sep}, pages={2627–2648} }
 @article{banks_flores_langlois_serio_sindi_2017, title={Estimating the rate of prion aggregate amplification in yeast with a generation and structured population model}, volume={26}, ISSN={1741-5977 1741-5985}, url={http://dx.doi.org/10.1080/17415977.2017.1316498}, DOI={10.1080/17415977.2017.1316498}, abstractNote={Prions are a special class of proteins capable of adopting multiple (misfolded) conformations, some of which have been associated with fatal diseases in mammals such as bovine spongiform encephalopathy or Creutzfeldt–Jakob Disease. Prion diseases, like protein misfolding diseases in general, are caused by the formation and amplification of ordered aggregates of proteins called amyloids. While such diseases in mammals can take decades to form, yeast have a variety of prion phenotypes that occur over a few hours, making this system an ideal model for protein misfolding disease in general. Most experimental assays of colonies with yeast prions provide steady-state population observations which complicate the inference of biochemical parameters both by the inability to directly measure aggregate amplification and by obscuring heterogeneity between cells. We develop a mathematical and inverse problem formulation to determine the amplification rate with prion aggregates from single-cell measurements observed in propagon amplification experiments. We demonstrate the ability of our formulation to determine heterogeneous amplification rates on simulated and experimental data. Our results show that aggregate amplification rates for two prion variants are strongly bimodal, suggesting that the generational structure in the yeast population impacts the ability of prion aggregates to amplify.}, number={2}, journal={Inverse Problems in Science and Engineering}, publisher={Informa UK Limited}, author={Banks, H. T. and Flores, Kevin B. and Langlois, Christine R. and Serio, Tricia R. and Sindi, Suzanne S.}, year={2017}, month={Apr}, pages={257–279} }
 @article{hamilton_lloyd_flores_2017, title={Hybrid modeling and prediction of dynamical systems}, volume={13}, number={7}, journal={PLoS Computational Biology}, author={Hamilton, F. and Lloyd, A. L. and Flores, K. B.}, year={2017} }
 @article{banks_collins_flores_pershad_stemkovski_stephenson_2017, title={Statistical error model comparison for logistic growth of green algae (Raphidocelis subcapitata)}, volume={64}, ISSN={0893-9659}, url={http://dx.doi.org/10.1016/J.AML.2016.09.006}, DOI={10.1016/J.AML.2016.09.006}, abstractNote={We validate a model for the population dynamics, as they occur in a chemostat environment, of the green algae Raphidocelis subcapitata, a species that is often used as a primary food source in toxicity experiments for the fresh water crustacean Daphnia magna. We collected longitudinal data from 4 replicate population experiments with R. subcapitata. This data was fit to a logistic growth model to reveal patterns of the algae growth in a continuous culture. Overall, our results suggest that a proportional error statistical model is the most appropriate for logistic growth modeling of R. subcapitata continuous population growth.}, journal={Applied Mathematics Letters}, publisher={Elsevier BV}, author={Banks, H.T. and Collins, Elizabeth and Flores, Kevin and Pershad, Prayag and Stemkovski, Michael and Stephenson, Lyric}, year={2017}, month={Feb}, pages={213–222} }
 @article{wang_wu_flores_lai_wang_2016, title={Build to understand: synthetic approaches to biology}, volume={8}, ISSN={1757-9694 1757-9708}, url={http://dx.doi.org/10.1039/c5ib00252d}, DOI={10.1039/c5ib00252d}, abstractNote={In this review we discuss how synthetic biology facilitates the task of investigating genetic circuits that are observed in naturally occurring biological systems.}, number={4}, journal={Integrative Biology}, publisher={Oxford University Press (OUP)}, author={Wang, Le-Zhi and Wu, Fuqing and Flores, Kevin and Lai, Ying-Cheng and Wang, Xiao}, year={2016}, pages={394–408} }
 @article{banks_flores_sindi_2016, title={On analytical and numerical approaches to division and label structured population models}, volume={60}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2016.04.009}, abstractNote={Even among cells in the same population, the concentration of a protein or cellular constituent can vary considerably. This heterogeneity can arise from several sources, including differences in kinetic rates between cells and distribution of cellular constituents through cell division. Compartmental models have been used to describe the distribution of the number of divisions undergone by cells in a population. More recently, such models have been coupled with the dynamics of intracellular labels and analytical solutions to the division and label structured population equations have been found. However, such approaches have thus far focused on simple models of intracellular dynamics such as the decay of an intracellular label. In this work, we demonstrate that analytical solutions are possible for more general forms of intracellular dynamics offering the promise to lend mathematical insight into population dynamics in more realistic biological settings.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. T. and Flores, Kevin B. and Sindi, Suzanne S.}, year={2016}, month={Oct}, pages={81–88} }
 @article{stemkovski_baraldi_flores_banks_2016, title={Validation of a mathematical model for green algae (Raphidocelis Subcapitata) growth and implications for a coupled dynamical system with Daphnia magna}, volume={6}, number={5}, journal={Applied Sciences-Basel}, author={Stemkovski, M. and Baraldi, R. and Flores, K. B. and Banks, H. T.}, year={2016} }
 @article{adoteye_baraldi_flores_nardini_banks_thompson_2015, title={Correlation of parameter estimators for models admitting multiple parametrizations}, volume={105}, ISSN={1311-8080 1314-3395}, url={http://dx.doi.org/10.12732/ijpam.v105i3.16}, DOI={10.12732/ijpam.v105i3.16}, number={3}, journal={International Journal of Pure and Applied Mathematics}, publisher={Academic Publications}, author={Adoteye, K and Baraldi, R and Flores, K and Nardini, J and Banks, HT and Thompson, WC}, year={2015}, month={Dec}, pages={497–522} }
 @article{adoteye_banks_flores_leblanc_2015, title={Estimation of time-varying mortality rates using continuous models for Daphnia magna}, volume={44}, ISSN={["1873-5452"]}, DOI={10.1016/j.aml.2014.12.014}, abstractNote={Structured population models that make the assumption of constant demographic rates do not accurately describe the complex life histories seen in many species. We investigated the accuracy of using constant versus time-varying mortality rates within discrete and continuously structured models for Daphnia magna. We tested the accuracy of the models we considered using density-independent survival data for 90 daphnids. We found that a continuous differential equation model with a time-varying mortality rate was the most accurate model for describing our experimental D. magna survival data. Our results suggest that differential equation models with variable parameters are an accurate tool for estimating mortality rates in biological scenarios in which mortality might vary significantly with age.}, journal={APPLIED MATHEMATICS LETTERS}, author={Adoteye, Kaska and Banks, H. T. and Flores, Kevin B. and LeBlanc, Gerald A.}, year={2015}, month={Jun}, pages={12–16} }
 @article{banks_flores_hu_rosenberg_buzon_yu_lichterfeld_2015, title={Immuno-modulatory strategies for reduction of HIV reservoir cells}, volume={372}, ISSN={["1095-8541"]}, DOI={10.1016/j.jtbi.2015.02.006}, abstractNote={Antiretroviral therapy is able to suppress the viral load to below the detection limit, but it is not able to eradicate HIV reservoirs. Thus, there is a critical need for a novel treatment to eradicate (or reduce) the reservoir in order to eliminate the need for a lifelong adherence to antiretroviral therapy, which is expensive and potentially toxic. In this paper, we investigate the possible pharmacological strategies or combinations of strategies that may be beneficial to reduce or possibly eradicate the latent reservoir. We do this via studies with a validated mathematical model, where the parameter values are obtained with newly acquired clinical data for HIV patients. Our findings indicate that the strategy of reactivating the reservoir combined with enhancement of the killing rate of HIV-specific CD8+ T cells is able to eradicate the reservoir. In addition, our analysis shows that a targeted suppression of the immune system is also a possible strategy to eradicate the reservoir.}, journal={JOURNAL OF THEORETICAL BIOLOGY}, author={Banks, H. T. and Flores, Kevin B. and Hu, Shuhua and Rosenberg, Eric and Buzon, Maria and Yu, Xu and Lichterfeld, Matthias}, year={2015}, month={May}, pages={146–158} }
 @article{banks_baraldi_flores_2015, title={Optimal design for minimizing uncertainty in dynamic equilibrium systems}, volume={3}, number={1}, journal={Eurasian Journal of Mathematical and Computer Applications}, author={Banks, H.T. and Baraldi, R. and Flores, K.B.}, year={2015}, pages={23–47} }
 @article{adoteye_banks_flores_2015, title={Optimal design of non-equilibrium experiments for genetic network interrogation}, volume={40}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2014.09.013}, abstractNote={Many experimental systems in biology, especially synthetic gene networks, are amenable to perturbations that are controlled by the experimenter. We developed an optimal design algorithm that calculates optimal observation times in conjunction with optimal experimental perturbations in order to maximize the amount of information gained from longitudinal data derived from such experiments. We applied the algorithm to a validated model of a synthetic Brome Mosaic Virus (BMV) gene network and found that optimizing experimental perturbations may substantially decrease uncertainty in estimating BMV model parameters.}, journal={APPLIED MATHEMATICS LETTERS}, author={Adoteye, Kaska and Banks, H. T. and Flores, Kevin B.}, year={2015}, month={Feb}, pages={84–89} }
 @article{adoteye_banks_cross_eytcheson_flores_leblanc_nguyen_ross_smith_stemkovski_et al._2015, title={Statistical validation of structured population models for Daphnia magna}, volume={266}, ISSN={0025-5564}, url={http://dx.doi.org/10.1016/j.mbs.2015.06.003}, DOI={10.1016/j.mbs.2015.06.003}, abstractNote={In this study we use statistical validation techniques to verify density-dependent mechanisms hypothesized for populations of Daphnia magna. We develop structured population models that exemplify specific mechanisms and use multi-scale experimental data in order to test their importance. We show that fecundity and survival rates are affected by both time-varying density-independent factors, such as age, and density-dependent factors, such as competition. We perform uncertainty analysis and show that our parameters are estimated with a high degree of confidence. Furthermore, we perform a sensitivity analysis to understand how changes in fecundity and survival rates affect population size and age-structure.}, journal={Mathematical Biosciences}, publisher={Elsevier BV}, author={Adoteye, Kaska and Banks, H.T. and Cross, Karissa and Eytcheson, Stephanie and Flores, Kevin B. and LeBlanc, Gerald A. and Nguyen, Timothy and Ross, Chelsea and Smith, Emmaline and Stemkovski, Michael and et al.}, year={2015}, month={Aug}, pages={73–84} }
 @article{sadd_barribeau_bloch_graaf_dearden_elsik_gadau_grimmelikhuijzen_hasselmann_lozier_et al._2015, title={The genomes of two key bumblebee species with primitive eusocial organization}, volume={16}, journal={Genome Biology}, author={Sadd, B. M. and Barribeau, S. M. and Bloch, G. and Graaf, D. C. and Dearden, P. and Elsik, C. G. and Gadau, J. and Grimmelikhuijzen, C. J. P. and Hasselmann, M. and Lozier, J. D. and et al.}, year={2015} }
 @article{banks_baraldi_cross_flores_mcchesney_poag_thorpe_2015, title={UNCERTAINTY QUANTIFICATION IN MODELING HIV VIRAL MECHANICS}, volume={12}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2015.12.937}, abstractNote={We consider an in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work [7]. We revisit the earlier model in light of progress over the last several years in understanding HIV-1 progression in humans. We then consider statistical models to describe the data and use these with residual plots in generalized least squares problems to develop accurate descriptions of the proper weights for the data. We use recent parameter subset selection techniques [5,6] to investigate the impact of estimated parameters on the corresponding selection scores. Bootstrapping and asymptotic theory are compared in the context of confidence intervals for the resulting parameter estimates.}, number={5}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Baraldi, Robert and Cross, Karissa and Flores, Kevin and Mcchesney, Christina and Poag, Laura and Thorpe, Emma}, year={2015}, month={Oct}, pages={937–964} }
 @inproceedings{baraldi_cross_mcchesney_poag_thorpe_flores_banks_2014, title={Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions}, booktitle={2014 american control conference (acc)}, author={Baraldi, R. and Cross, K. and McChesney, C. and Poag, L. and Thorpe, E. and Flores, K. B. and Banks, H. T.}, year={2014}, pages={2753–2758} }
 @article{huffman_link_nardini_poag_flores_banks_blasco_jungfleisch_diez_2013, title={A mathematical model of RNA3 recruitment in the replication cycle of Brome Mosaic Virus}, volume={89}, ISSN={1311-8080 1314-3395}, url={http://dx.doi.org/10.12732/ijpam.v89i2.9}, DOI={10.12732/ijpam.v89i2.9}, number={2}, journal={International Journal of Pure and Applied Mathematics}, publisher={Academic Publications}, author={Huffman, T. and Link, K. and Nardini, J. and Poag, L. and Flores, K. and Banks, H.T. and Blasco, B. and Jungfleisch, J. and Diez, J.}, year={2013}, month={Dec}, pages={251–274} }
 @article{flores_2013, title={A structured population modeling framework for quantifying and predicting gene expression noise in flow cytometry data}, volume={26}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2013.03.003}, abstractNote={We formulated a structured population model with distributed parameters to identify mechanisms that contribute to gene expression noise in time-dependent flow cytometry data. The model was validated using cell population-level gene expression data from two experiments with synthetically engineered eukaryotic cells. Our model captures the qualitative noise features of both experiments and accurately fit the data from the first experiment. Our results suggest that cellular switching between high and low expression states and transcriptional re-initiation are important factors needed to accurately describe gene expression noise with a structured population model.}, number={7}, journal={APPLIED MATHEMATICS LETTERS}, author={Flores, Kevin B.}, year={2013}, month={Jul}, pages={794–798} }
 @article{everett_zhao_flores_kuang_2013, title={DATA AND IMPLICATION BASED COMPARISON OF TWO CHRONIC MYELOID LEUKEMIA MODELS}, volume={10}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2013.10.1501}, abstractNote={Chronic myeloid leukemia, a disorder of hematopoietic stem cells, is currently treated using targeted molecular therapy with imatinib. We compare two models that describe the treatment of CML, a multi-scale model (Model 1) and a simple cell competition model (Model 2).Both models describe the competition of leukemic and normal cells, however Model 1 also describes the dynamics of BCR-ABL, the oncogene targeted by imatinib, at the sub-cellular level. Using clinical data, we analyze the differences in estimated parameters between the models and the capacity for each model to predict drug resistance. We found that while both models fit the data well, Model 1 is more biologically relevant. The estimated parameter ranges for Model 2 are unrealistic, whereas the parameter ranges for Model 1 are close to values found in literature. We also found that Model 1 predicts long-term drug resistance from patient data, which is exhibited by both an increase in the proportion of leukemic cells as well as an increase in BCR-ABL/ABL%. Model 2, however, is not able to predict resistance and accurately model the clinical data. These results suggest that including sub-cellular mechanisms in a mathematical model of CML can increase the accuracy of parameter estimation and may help to predict long-term drug resistance.}, number={5-6}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Everett, R. A. and Zhao, Y. and Flores, K. B. and Kuang, Y.}, year={2013}, pages={1501–1518} }
 @article{flores_wolschin_amdam_2013, title={The Role of Methylation of DNA in Environmental Adaptation}, volume={53}, ISSN={1540-7063 1557-7023}, url={http://dx.doi.org/10.1093/icb/ict019}, DOI={10.1093/icb/ict019}, abstractNote={Methylation of DNA is an epigenetic mechanism that influences patterns of gene expression. DNA methylation marks contribute to adaptive phenotypic variation but are erased during development. The role of DNA methylation in adaptive evolution is therefore unclear. We propose that environmentally-induced DNA methylation causes phenotypic heterogeneity that provides a substrate for selection via forces that act on the epigenetic machinery. For example, selection can alter environmentally-induced methylation of DNA by acting on the molecular mechanisms used for the genomic targeting of DNA methylation. Another possibility is that specific methylation marks that are environmentally-induced, yet non-heritable, could influence preferential survival and lead to consistent methylation of the same genomic regions over time. As methylation of DNA is known to increase the likelihood of cytosine-to-thymine transitions, non-heritable adaptive methylation marks can drive an increased likelihood of mutations targeted to regions that are consistently marked across several generations. Some of these mutations could capture, genetically, the phenotypic advantage of the epigenetic mark. Thereby, selectively favored transitory alterations in the genome invoked by DNA methylation could ultimately become selectable genetic variation through mutation. We provide evidence for these concepts using examples from different taxa, but focus on experimental data on large-scale DNA sequencing that expose between-group genetic variation after bidirectional selection on honeybees, Apis mellifera.}, number={2}, journal={Integrative and Comparative Biology}, publisher={Oxford University Press (OUP)}, author={Flores, K. B. and Wolschin, F. and Amdam, G. V.}, year={2013}, month={Apr}, pages={359–372} }
 @article{flores_wolschin_corneveaux_allen_huentelman_amdam_2012, title={Genome-wide association between DNA methylation and alternative splicing in an invertebrate}, volume={13}, ISSN={1471-2164}, url={http://dx.doi.org/10.1186/1471-2164-13-480}, DOI={10.1186/1471-2164-13-480}, abstractNote={Gene bodies are the most evolutionarily conserved targets of DNA methylation in eukaryotes. However, the regulatory functions of gene body DNA methylation remain largely unknown. DNA methylation in insects appears to be primarily confined to exons. Two recent studies in Apis mellifera (honeybee) and Nasonia vitripennis (jewel wasp) analyzed transcription and DNA methylation data for one gene in each species to demonstrate that exon-specific DNA methylation may be associated with alternative splicing events. In this study we investigated the relationship between DNA methylation, alternative splicing, and cross-species gene conservation on a genome-wide scale using genome-wide transcription and DNA methylation data. We generated RNA deep sequencing data (RNA-seq) to measure genome-wide mRNA expression at the exon- and gene-level. We produced a de novo transcriptome from this RNA-seq data and computationally predicted splice variants for the honeybee genome. We found that exons that are included in transcription are higher methylated than exons that are skipped during transcription. We detected enrichment for alternative splicing among methylated genes compared to unmethylated genes using fisher’s exact test. We performed a statistical analysis to reveal that the presence of DNA methylation or alternative splicing are both factors associated with a longer gene length and a greater number of exons in genes. In concordance with this observation, a conservation analysis using BLAST revealed that each of these factors is also associated with higher cross-species gene conservation. This study constitutes the first genome-wide analysis exhibiting a positive relationship between exon-level DNA methylation and mRNA expression in the honeybee. Our finding that methylated genes are enriched for alternative splicing suggests that, in invertebrates, exon-level DNA methylation may play a role in the construction of splice variants by positively influencing exon inclusion during transcription. The results from our cross-species homology analysis suggest that DNA methylation and alternative splicing are genetic mechanisms whose utilization could contribute to a longer gene length and a slower rate of gene evolution.}, number={1}, journal={BMC Genomics}, publisher={Springer Nature}, author={Flores, Kevin and Wolschin, Florian and Corneveaux, Jason J and Allen, April N and Huentelman, Matthew J and Amdam, Gro V}, year={2012}, pages={480} }
 @article{flores_amdam_2011, title={Deciphering a methylome: what can we read into patterns of DNA methylation?}, volume={214}, ISSN={0022-0949 1477-9145}, url={http://dx.doi.org/10.1242/jeb.059741}, DOI={10.1242/jeb.059741}, abstractNote={Summary The methylation of cytosines within cytosine–guanine (CG) dinucleotides is an epigenetic mark that can modify gene transcription. With the advent of high-throughput sequencing, it is possible to map methylomes, i.e. detect methylated CGs on a genome-wide scale. The methylomes sequenced to date reveal a divergence in prevalence and targeting of CG methylation between taxa, despite the conservation of the DNA methyltransferase enzymes that cause DNA methylation. Therefore, interspecific methylation usage is predicted to diverge. In various taxa, this tenet gains support from patterns of CG depletion that can be traced in DNA before methylomes are explicitly mapped. Depletion of CGs in methylated genomic regions is expected because methylated cytosines are subject to increased mutability caused by nucleotide deamination. However, the basis of diverging interspecific methylation usage is less clear. We use insights from the methylome of honeybees (Apis mellifera) to emphasize the possible importance of organismal life histories in explaining methylation usage and the accuracy of methylation prediction based on CG depletion. Interestingly, methylated genes in honeybees are more conserved across taxa than non-methylated genes despite the divergence in utilization of methylation and the increased mutability caused by deamination.}, number={19}, journal={Journal of Experimental Biology}, publisher={The Company of Biologists}, author={Flores, K. B. and Amdam, G. V.}, year={2011}, month={Sep}, pages={3155–3163} }
 @article{flores_hadeler_2010, title={The random walk of Azospirillum brasilense}, volume={4}, ISSN={1751-3758 1751-3766}, url={http://dx.doi.org/10.1080/17513750902773914}, DOI={10.1080/17513750902773914}, abstractNote={The bacterium Azospirillum brasilense has been frequently studied in laboratory experiments. It performs movements in space where long forward and backward runs on a straight line occur simultaneously with slow changes of direction of the line. A model is presented in which a correlated random walk on a line is joined to diffusion on a sphere of directions. For this transport system, a hierarchy of moment approximations is derived, ranging from a hyperbolic system with four dependent variables to a scalar damped wave equation (telegraph equation) and then to a single diffusion equation for particle density. The original parameters are compounded in the diffusion quotient. The effects of these parameters, such as particle speed or turning rate, on the diffusion coefficient are discussed in detail.}, number={1}, journal={Journal of Biological Dynamics}, publisher={Informa UK Limited}, author={Flores, Kevin and Hadeler, K. P.}, year={2010}, month={Jan}, pages={71–85} }