Dose-response modeling in high-throughput cancer drug screenings: an end-to-end approach.

Personalized cancer treatments based on the molecular profile of a patient's tumor are an emerging and exciting class of treatments in oncology. As genomic tumor profiling is becoming more common, targeted treatments for specific molecular alterations are gaining traction. To discover new potential therapeutics that may apply to broad classes of tumors matching some molecular pattern, experimentalists and pharmacologists rely on high-throughput, in vitro screens of many compounds against many different cell lines. We propose a hierarchical Bayesian model of how cancer cell lines respond to drugs in these experiments and develop a method for fitting the model to real-world high-throughput screening data. Through a case study, the model is shown to capture nontrivial associations between molecular features and drug response, such as requiring both wild type TP53 and overexpression of MDM2 to be sensitive to Nutlin-3(a). In quantitative benchmarks, the model outperforms a standard approach in biology, with $\approx20\%$ lower predictive error on held out data. When combined with a conditional randomization testing procedure, the model discovers markers of therapeutic response that recapitulate known biology and suggest new avenues for investigation. All code for the article is publicly available at https://github.com/tansey/deep-dose-response.

Multimodal transcriptional control of pattern formation in embryonic development.

Predicting how interactions between transcription factors and regulatory DNA sequence dictate rates of transcription and, ultimately, drive developmental outcomes remains an open challenge in physical biology. Using stripe 2 of the even-skipped gene in Drosophila embryos as a case study, we dissect the regulatory forces underpinning a key step along the developmental decision-making cascade: the generation of cytoplasmic mRNA patterns via the control of transcription in individual cells. Using live imaging and computational approaches, we found that the transcriptional burst frequency is modulated across the stripe to control the mRNA production rate. However, we discovered that bursting alone cannot quantitatively recapitulate the formation of the stripe and that control of the window of time over which each nucleus transcribes even-skipped plays a critical role in stripe formation. Theoretical modeling revealed that these regulatory strategies (bursting and the time window) respond in different ways to input transcription factor concentrations, suggesting that the stripe is shaped by the interplay of 2 distinct underlying molecular processes.

Noise Expands the Response Range of the Bacillus subtilis Competence Circuit.

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit.

Multiple LacI-mediated loops revealed by Bayesian statistics and tethered particle motion.

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple coexisting loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e. DNA-protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA-binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein-nucleic acid interactions.

Statistical inference for nanopore sequencing with a biased random walk model.

Nanopore sequencing promises long read-lengths and single-molecule resolution, but the stochastic motion of the DNA molecule inside the pore is, as of this writing, a barrier to high accuracy reads. We develop a method of statistical inference that explicitly accounts for this error, and demonstrate that high accuracy (>99%) sequence inference is feasible even under highly diffusive motion by using a hidden Markov model to jointly analyze multiple stochastic reads. Using this model, we place bounds on achievable inference accuracy under a range of experimental parameters.

Single-molecule dataset (SMD): a generalized storage format for raw and processed single-molecule data.

BACKGROUND: Single-molecule techniques have emerged as incisive approaches for addressing a wide range of questions arising in contemporary biological research [Trends Biochem Sci 38:30-37, 2013; Nat Rev Genet 14:9-22, 2013; Curr Opin Struct Biol 2014, 28C:112-121; Annu Rev Biophys 43:19-39, 2014]. The analysis and interpretation of raw single-molecule data benefits greatly from the ongoing development of sophisticated statistical analysis tools that enable accurate inference at the low signal-to-noise ratios frequently associated with these measurements. While a number of groups have released analysis toolkits as open source software [J Phys Chem B 114:5386-5403, 2010; Biophys J 79:1915-1927, 2000; Biophys J 91:1941-1951, 2006; Biophys J 79:1928-1944, 2000; Biophys J 86:4015-4029, 2004; Biophys J 97:3196-3205, 2009; PLoS One 7:e30024, 2012; BMC Bioinformatics 288 11(8):S2, 2010; Biophys J 106:1327-1337, 2014; Proc Int Conf Mach Learn 28:361-369, 2013], it remains difficult to compare analysis for experiments performed in different labs due to a lack of standardization. RESULTS: Here we propose a standardized single-molecule dataset (SMD) file format. SMD is designed to accommodate a wide variety of computer programming languages, single-molecule techniques, and analysis strategies. To facilitate adoption of this format we have made two existing data analysis packages that are used for single-molecule analysis compatible with this format. CONCLUSION: Adoption of a common, standard data file format for sharing raw single-molecule data and analysis outcomes is a critical step for the emerging and powerful single-molecule field, which will benefit both sophisticated users and non-specialists by allowing standardized, transparent, and reproducible analysis practices.

Learning probabilistic phenotypes from heterogeneous EHR data.

We present the Unsupervised Phenome Model (UPhenome), a probabilistic graphical model for large-scale discovery of computational models of disease, or phenotypes. We tackle this challenge through the joint modeling of a large set of diseases and a large set of clinical observations. The observations are drawn directly from heterogeneous patient record data (notes, laboratory tests, medications, and diagnosis codes), and the diseases are modeled in an unsupervised fashion. We apply UPhenome to two qualitatively different mixtures of patients and diseases: records of extremely sick patients in the intensive care unit with constant monitoring, and records of outpatients regularly followed by care providers over multiple years. We demonstrate that the UPhenome model can learn from these different care settings, without any additional adaptation. Our experiments show that (i) the learned phenotypes combine the heterogeneous data types more coherently than baseline LDA-based phenotypes; (ii) they each represent single diseases rather than a mix of diseases more often than the baseline ones; and (iii) when applied to unseen patient records, they are correlated with the patients' ground-truth disorders. Code for training, inference, and quantitative evaluation is made available to the research community.

Empirical Bayes methods enable advanced population-level analyses of single-molecule FRET experiments.

Many single-molecule experiments aim to characterize biomolecular processes in terms of kinetic models that specify the rates of transition between conformational states of the biomolecule. Estimation of these rates often requires analysis of a population of molecules, in which the conformational trajectory of each molecule is represented by a noisy, time-dependent signal trajectory. Although hidden Markov models (HMMs) may be used to infer the conformational trajectories of individual molecules, estimating a consensus kinetic model from the population of inferred conformational trajectories remains a statistically difficult task, as inferred parameters vary widely within a population. Here, we demonstrate how a recently developed empirical Bayesian method for HMMs can be extended to enable a more automated and statistically principled approach to two widely occurring tasks in the analysis of single-molecule fluorescence resonance energy transfer (smFRET) experiments: 1), the characterization of changes in rates across a series of experiments performed under variable conditions; and 2), the detection of degenerate states that exhibit the same FRET efficiency but differ in their rates of transition. We apply this newly developed methodology to two studies of the bacterial ribosome, each exemplary of one of these two analysis tasks. We conclude with a discussion of model-selection techniques for determination of the appropriate number of conformational states. The code used to perform this analysis and a basic graphical user interface front end are available as open source software.

Statistical method for revealing form-function relations in biological networks.

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions--lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.

A stochastic spectral analysis of transcriptional regulatory cascades.

The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here, we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The spectral method exploits the natural eigenfunctions of the master equation of birth-death processes to solve for the joint distribution of modules within the network, which then inform each other and facilitate calculation of the entire joint distribution. We illustrate the method on a ubiquitous case in nature: linear regulatory cascades. The efficiency of the method makes possible numerical optimization of the input and regulatory parameters, revealing design properties of, e.g., the most informative cascades. We find, for threshold regulation, that a cascade of strong regulations converts a unimodal input to a bimodal output, that multimodal inputs are no more informative than bimodal inputs, and that a chain of up-regulations outperforms a chain of down-regulations. We anticipate that this numerical approach may be useful for modeling noise in a variety of small network topologies in biology.

Allosteric collaboration between elongation factor G and the ribosomal L1 stalk directs tRNA movements during translation.

Determining the mechanism by which tRNAs rapidly and precisely transit through the ribosomal A, P, and E sites during translation remains a major goal in the study of protein synthesis. Here, we report the real-time dynamics of the L1 stalk, a structural element of the large ribosomal subunit that is implicated in directing tRNA movements during translation. Within pretranslocation ribosomal complexes, the L1 stalk exists in a dynamic equilibrium between open and closed conformations. Binding of elongation factor G (EF-G) shifts this equilibrium toward the closed conformation through one of at least two distinct kinetic mechanisms, where the identity of the P-site tRNA dictates the kinetic route that is taken. Within posttranslocation complexes, L1 stalk dynamics are dependent on the presence and identity of the E-site tRNA. Collectively, our data demonstrate that EF-G and the L1 stalk allosterically collaborate to direct tRNA translocation from the P to the E sites, and suggest a model for the release of E-site tRNA.

Learning "graph-mer" motifs that predict gene expression trajectories in development.

A key problem in understanding transcriptional regulatory networks is deciphering what cis regulatory logic is encoded in gene promoter sequences and how this sequence information maps to expression. A typical computational approach to this problem involves clustering genes by their expression profiles and then searching for overrepresented motifs in the promoter sequences of genes in a cluster. However, genes with similar expression profiles may be controlled by distinct regulatory programs. Moreover, if many gene expression profiles in a data set are highly correlated, as in the case of whole organism developmental time series, it may be difficult to resolve fine-grained clusters in the first place. We present a predictive framework for modeling the natural flow of information, from promoter sequence to expression, to learn cis regulatory motifs and characterize gene expression patterns in developmental time courses. We introduce a cluster-free algorithm based on a graph-regularized version of partial least squares (PLS) regression to learn sequence patterns--represented by graphs of k-mers, or "graph-mers"--that predict gene expression trajectories. Applying the approach to wildtype germline development in Caenorhabditis elegans, we found that the first and second latent PLS factors mapped to expression profiles for oocyte and sperm genes, respectively. We extracted both known and novel motifs from the graph-mers associated to these germline-specific patterns, including novel CG-rich motifs specific to oocyte genes. We found evidence supporting the functional relevance of these putative regulatory elements through analysis of positional bias, motif conservation and in situ gene expression. This study demonstrates that our regression model can learn biologically meaningful latent structure and identify potentially functional motifs from subtle developmental time course expression data.

A predictive model for next cycle start date that accounts for adherence in menstrual self-tracking.

OBJECTIVE: The study sought to build predictive models of next menstrual cycle start date based on mobile health self-tracked cycle data. Because app users may skip tracking, disentangling physiological patterns of menstruation from tracking behaviors is necessary for the development of predictive models. MATERIALS AND METHODS: We use data from a popular menstrual tracker (186 000 menstruators with over 2 million tracked cycles) to learn a predictive model, which (1) accounts explicitly for self-tracking adherence; (2) updates predictions as a given cycle evolves, allowing for interpretable insight into how these predictions change over time; and (3) enables modeling of an individual's cycle length history while incorporating population-level information. RESULTS: Compared with 5 baselines (mean, median, convolutional neural network, recurrent neural network, and long short-term memory network), the model yields better predictions and consistently outperforms them as the cycle evolves. The model also provides predictions of skipped tracking probabilities. DISCUSSION: Mobile health apps such as menstrual trackers provide a rich source of self-tracked observations, but these data have questionable reliability, as they hinge on user adherence to the app. By taking a machine learning approach to modeling self-tracked cycle lengths, we can separate true cycle behavior from user adherence, allowing for more informed predictions and insights into the underlying observed data structure. CONCLUSIONS: Disentangling physiological patterns of menstruation from adherence allows for accurate and informative predictions of menstrual cycle start date and is necessary for mobile tracking apps. The proposed predictive model can support app users in being more aware of their self-tracking behavior and in better understanding their cycle dynamics.

A Generative Modeling Approach to Calibrated Predictions: A Use Case on Menstrual Cycle Length Prediction.

We explore how to quantify uncertainty when designing predictive models for healthcare to provide well-calibrated results. Uncertainty quantification and calibration are critical in medicine, as one must not only accommodate the variability of the underlying physiology, but adjust to the uncertain data collection and reporting process. This occurs not only on the context of electronic health records (i.e., the clinical documentation process), but on mobile health as well (i.e., user specific self-tracking patterns must be accounted for). In this work, we show that accurate uncertainty estimation is directly relevant to an important health application: the prediction of menstrual cycle length, based on self-tracked information. We take advantage of a flexible generative model that accommodates under-dispersed distributions via two degrees of freedom to fit the mean and variance of the observed cycle lengths. From a machine learning perspective, our work showcases how flexible generative models can not only provide state-of-the art predictive accuracy, but enable well-calibrated predictions. From a healthcare perspective, we demonstrate that with flexible generative models, not only can we accommodate the idiosyncrasies of mobile health data, but we can also adjust the predictive uncertainty to per-user cycle length patterns. We evaluate the proposed model in real-world cycle length data collected by one of the most popular menstrual trackers worldwide, and demonstrate how the proposed generative model provides accurate and well-calibrated cycle length predictions. Providing meaningful, less uncertain cycle length predictions is beneficial for menstrual health researchers, mobile health users and developers, as it may help design more usable mobile health solutions.

Graphical models for inferring single molecule dynamics.

BACKGROUND: The recent explosion of experimental techniques in single molecule biophysics has generated a variety of novel time series data requiring equally novel computational tools for analysis and inference. This article describes in general terms how graphical modeling may be used to learn from biophysical time series data using the variational Bayesian expectation maximization algorithm (VBEM). The discussion is illustrated by the example of single-molecule fluorescence resonance energy transfer (smFRET) versus time data, where the smFRET time series is modeled as a hidden Markov model (HMM) with Gaussian observables. A detailed description of smFRET is provided as well. RESULTS: The VBEM algorithm returns the model's evidence and an approximating posterior parameter distribution given the data. The former provides a metric for model selection via maximum evidence (ME), and the latter a description of the model's parameters learned from the data. ME/VBEM provide several advantages over the more commonly used approach of maximum likelihood (ML) optimized by the expectation maximization (EM) algorithm, the most important being a natural form of model selection and a well-posed (non-divergent) optimization problem. CONCLUSIONS: The results demonstrate the utility of graphical modeling for inference of dynamic processes in single molecule biophysics.

Information-optimal transcriptional response to oscillatory driving.

Intracellular transmission of information via chemical and transcriptional networks is thwarted by a physical limitation: The finite copy number of the constituent chemical species introduces unavoidable intrinsic noise. Here we solve for the complete probabilistic description of the intrinsically noisy response to an oscillatory driving signal. We derive and numerically verify a number of simple scaling laws. Unlike in the case of measuring a static quantity, response to an oscillatory signal can exhibit a resonant frequency which maximizes information transmission. Furthermore, we show that the optimal regulatory design is dependent on biophysical constraints (i.e., the allowed copy number and response time). The resulting phase diagram illustrates under what conditions threshold regulation outperforms linear regulation.

Characterizing physiological and symptomatic variation in menstrual cycles using self-tracked mobile-health data.

The menstrual cycle is a key indicator of overall health for women of reproductive age. Previously, menstruation was primarily studied through survey results; however, as menstrual tracking mobile apps become more widely adopted, they provide an increasingly large, content-rich source of menstrual health experiences and behaviors over time. By exploring a database of user-tracked observations from the Clue app by BioWink GmbH of over 378,000 users and 4.9 million natural cycles, we show that self-reported menstrual tracker data can reveal statistically significant relationships between per-person cycle length variability and self-reported qualitative symptoms. A concern for self-tracked data is that they reflect not only physiological behaviors, but also the engagement dynamics of app users. To mitigate such potential artifacts, we develop a procedure to exclude cycles lacking user engagement, thereby allowing us to better distinguish true menstrual patterns from tracking anomalies. We uncover that women located at different ends of the menstrual variability spectrum, based on the consistency of their cycle length statistics, exhibit statistically significant differences in their cycle characteristics and symptom tracking patterns. We also find that cycle and period length statistics are stationary over the app usage timeline across the variability spectrum. The symptoms that we identify as showing statistically significant association with timing data can be useful to clinicians and users for predicting cycle variability from symptoms, or as potential health indicators for conditions like endometriosis. Our findings showcase the potential of longitudinal, high-resolution self-tracked data to improve understanding of menstruation and women's health as a whole.

Learning rates and states from biophysical time series: a Bayesian approach to model selection and single-molecule FRET data.

Time series data provided by single-molecule Förster resonance energy transfer (smFRET) experiments offer the opportunity to infer not only model parameters describing molecular complexes, e.g., rate constants, but also information about the model itself, e.g., the number of conformational states. Resolving whether such states exist or how many of them exist requires a careful approach to the problem of model selection, here meaning discrimination among models with differing numbers of states. The most straightforward approach to model selection generalizes the common idea of maximum likelihood--selecting the most likely parameter values--to maximum evidence: selecting the most likely model. In either case, such an inference presents a tremendous computational challenge, which we here address by exploiting an approximation technique termed variational Bayesian expectation maximization. We demonstrate how this technique can be applied to temporal data such as smFRET time series; show superior statistical consistency relative to the maximum likelihood approach; compare its performance on smFRET data generated from experiments on the ribosome; and illustrate how model selection in such probabilistic or generative modeling can facilitate analysis of closely related temporal data currently prevalent in biophysics. Source code used in this analysis, including a graphical user interface, is available open source via http://vbFRET.sourceforge.net.

Durable Interactions of T Cells with T Cell Receptor Stimuli in the Absence of a Stable Immunological Synapse.

T cells engage in two modes of interaction with antigen-presenting surfaces: stable synapses and motile kinapses. Although it is surmised that durable interactions of T cells with antigen-presenting cells involve synapses, in situ 3D imaging cannot resolve the mode of interaction. We have established in vitro 2D platforms and quantitative metrics to determine cell-intrinsic modes of interaction when T cells are faced with spatially continuous or restricted stimulation. All major resting human T cell subsets, except memory CD8 T cells, spend more time in the kinapse mode on continuous stimulatory surfaces. Surprisingly, we did not observe any concordant relationship between the mode and durability of interaction on cell-sized stimulatory spots. Naive CD8 T cells maintain kinapses for more than 3 hr before leaving stimulatory spots, whereas their memory counterparts maintain synapses for only an hour before leaving. Thus, durable interactions do not require stable synapses.

Benchmarking of dynamic Bayesian networks inferred from stochastic time-series data.

We seek to quantify the failure and success of dynamic Bayesian networks (DBNs), a popular tool for reverse-engineering networks from time-series data. In particular, we focus on data generated by continuous time processes (e.g., genetic expression) and sampled at discrete times. To facilitate analysis and interpretation, we employ a "minimal model" to generate arbitrary abundances of stochastic data from networks of known topologies, which are then sub-sampled and in some cases interpolated. We find that DBNs perform relatively poorly when given data sets comparable to those used for genetic network inference. Interpolation does not appear to improve inference success. Finally, we contrast the performance of DBNs with results from linear regression on our synthetic data.