Temporal Ordering of Cancer Microarray Data through a Reinforcement Learning Based Approach

Temporal modeling and analysis and more specifically, temporal ordering are very important problems within the fields of bioinformatics and computational biology, as the temporal analysis of the events characterizing a certain biological process could provide significant insights into its development and progression. Particularly, in the case of cancer, understanding the dynamics and the evolution of this disease could lead to better methods for prediction and treatment. In this paper we tackle, from a computational perspective, the temporal ordering problem, which refers to constructing a sorted collection of multi-dimensional biological data, collection that reflects an accurate temporal evolution of biological systems. We introduce a novel approach, based on reinforcement learning, more precisely, on Q-learning, for the biological temporal ordering problem. The experimental evaluation is performed using several DNA microarray data sets, two of which contain cancer gene expression data. The obtained solutions are correlated either to the given correct ordering (in the cases where this is provided for validation), or to the overall survival time of the patients (in the case of the cancer data sets), thus confirming a good performance of the proposed model and indicating the potential of our proposal.     

A mathematical methodology for determining the temporal order of pathway alterations arising during gliomagenesis

Human cancer is caused by the accumulation of genetic alterations in cells. Of special importance are changes that occur early during malignant transformation because they may result in oncogene addiction and thus represent promising targets for therapeutic intervention. We have previously described a computational approach, called Retracing the Evolutionary Steps in Cancer (RESIC), to determine the temporal sequence of genetic alterations during tumorigenesis from cross-sectional genomic data of tumors at their fully transformed stage. Since alterations within a set of genes belonging to a particular signaling pathway may have similar or equivalent effects, we applied a pathway-based systems biology approach to the RESIC methodology. This method was used to determine whether alterations of specific pathways develop early or late during malignant transformation. When applied to primary glioblastoma (GBM) copy number data from The Cancer Genome Atlas (TCGA) project, RESIC identified a temporal order of pathway alterations consistent with the order of events in secondary GBMs. We then further subdivided the samples into the four main GBM subtypes and determined the relative contributions of each subtype to the overall results: we found that the overall ordering applied for the proneural subtype but differed for mesenchymal samples. The temporal sequence of events could not be identified for neural and classical subtypes, possibly due to a limited number of samples. Moreover, for samples of the proneural subtype, we detected two distinct temporal sequences of events: (i) RAS pathway activation was followed by TP53 inactivation and finally PI3K2 activation, and (ii) RAS activation preceded only AKT activation. This extension of the RESIC methodology provides an evolutionary mathematical approach to identify the temporal sequence of pathway changes driving tumorigenesis and may be useful in guiding the understanding of signaling rearrangements in cancer development.     

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.     

The geometry of multisite phosphorylation

Reversible protein phosphorylation on multiple sites is a key regulatory mechanism in most cellular processes. We consider here a kinase-phosphatase-substrate system with two sites, under mass-action kinetics, with no restrictions on the order of phosphorylation or dephosphorylation. We show that the concentrations of the four phosphoforms at steady state satisfy an algebraic formula—an invariant—that is independent of the other chemical species, such as free enzymes or enzyme-substrate complexes, and holds irrespective of the starting conditions and the total amounts of enzymes and substrate. Such invariants allow stringent quantitative predictions to be made without requiring any knowledge of site-specific parameter values. We introduce what we believe are novel methods from algebraic geometry—Gröbner bases, rational curves—to calculate invariants. These methods are particularly significant because they make it possible to treat parameters symbolically without having to specify their numerical values, and thereby allow us to sidestep the parameter problem. We anticipate that this approach will have much wider applications in biological modeling.     

Conformational selection in protein binding and function

Protein binding and function often involves conformational changes. Advanced nuclear magnetic resonance (NMR) experiments indicate that these conformational changes can occur in the absence of ligand molecules (or with bound ligands), and that the ligands may “select” protein conformations for binding (or unbinding). In this review, we argue that this conformational selection requires transition times for ligand binding and unbinding that are small compared to the dwell times of proteins in different conformations, which is plausible for small ligand molecules. Such a separation of timescales leads to a decoupling and temporal ordering of binding/unbinding events and conformational changes. We propose that conformational‐selection and induced‐change processes (such as induced fit) are two sides of the same coin, because the temporal ordering is reversed in binding and unbinding direction. Conformational‐selection processes can be characterized by a conformational excitation that occurs prior to a binding or unbinding event, while induced‐change processes exhibit a characteristic conformational relaxation that occurs after a binding or unbinding event. We discuss how the ordering of events can be determined from relaxation rates and effective on‐ and off‐rates determined in mixing experiments, and from the conformational exchange rates measured in advanced NMR or single‐molecule fluorescence resonance energy transfer experiments. For larger ligand molecules such as peptides, conformational changes and binding events can be intricately coupled and exhibit aspects of conformational‐selection and induced‐change processes in both binding and unbinding direction.     

Evolution of early embryogenesis in rhabditid nematodes

The cell-biological events that guide early-embryonic development occur with great precision within species but can be quite diverse across species. How these cellular processes evolve and which molecular components underlie evolutionary changes is poorly understood. To begin to address these questions, we systematically investigated early embryogenesis, from the one- to the four-cell embryo, in 34 nematode species related to C. elegans. We found 40 cell-biological characters that captured the phenotypic differences between these species. By tracing the evolutionary changes on a molecular phylogeny, we found that these characters evolved multiple times and independently of one another. Strikingly, all these phenotypes are mimicked by single-gene RNAi experiments in C. elegans. We use these comparisons to hypothesize the molecular mechanisms underlying the evolutionary changes. For example, we predict that a cell polarity module was altered during the evolution of the Protorhabditis group and show that PAR-1, a kinase localized asymmetrically in C. elegans early embryos, is symmetrically localized in the one-cell stage of Protorhabditis group species. Our genome-wide approach identifies candidate molecules—and thereby modules—associated with evolutionary changes in cell-biological phenotypes.     

Characterization of early autophagy signaling by quantitative phosphoproteomics

Under conditions of nutrient shortage autophagy is the primary cellular mechanism ensuring availability of substrates for continuous biosynthesis. Subjecting cells to starvation or rapamycin efficiently induces autophagy by inhibiting the MTOR signaling pathway triggering increased autophagic flux. To elucidate the regulation of early signaling events upon autophagy induction, we applied quantitative phosphoproteomics characterizing the temporal phosphorylation dynamics after starvation and rapamycin treatment. We obtained a comprehensive atlas of phosphorylation kinetics within the first 30 min upon induction of autophagy with both treatments affecting widely different cellular processes. The identification of dynamic phosphorylation already after 2 min demonstrates that the earliest events in autophagy signaling occur rapidly after induction. The data was subjected to extensive bioinformatics analysis revealing regulated phosphorylation sites on proteins involved in a wide range of cellular processes and an impact of the treatments on the kinome. To approach the potential function of the identified phosphorylation sites we performed a screen for MAP1LC3-interacting proteins and identified a group of binding partners exhibiting dynamic phosphorylation patterns. The data presented here provide a valuable resource on phosphorylation events underlying early autophagy induction.     

The temporal order of genetic and pathway alterations in tumorigenesis

Cancer evolves through the accumulation of mutations, but the order in which mutations occur is poorly understood. Inference of a temporal ordering on the level of genes is challenging because clinically and histologically identical tumors often have few mutated genes in common. This heterogeneity may at least in part be due to mutations in different genes having similar phenotypic effects by acting in the same functional pathway. We estimate the constraints on the order in which alterations accumulate during cancer progression from cross-sectional mutation data using a probabilistic graphical model termed Hidden Conjunctive Bayesian Network (H-CBN). The possible orders are analyzed on the level of genes and, after mapping genes to functional pathways, also on the pathway level. We find stronger evidence for pathway order constraints than for gene order constraints, indicating that temporal ordering results from selective pressure acting at the pathway level. The accumulation of changes in core pathways differs among cancer types, yet a common feature is that progression appears to begin with mutations in genes that regulate apoptosis pathways and to conclude with mutations in genes involved in invasion pathways. H-CBN models provide a quantitative and intuitive model of tumorigenesis showing that the genetic events can be linked to the phenotypic progression on the level of pathways.     

Chromatin Hydrodynamics

Following recent observations of large scale correlated motion of chromatin inside the nuclei of live differentiated cells, we present a hydrodynamic theory—the two-fluid model—in which the content of a nucleus is described as a chromatin solution with the nucleoplasm playing the role of the solvent and the chromatin fiber that of a solute. This system is subject to both passive thermal fluctuations and active scalar and vector events that are associated with free energy consumption, such as ATP hydrolysis. Scalar events drive the longitudinal viscoelastic modes (where the chromatin fiber moves relative to the solvent) while vector events generate the transverse modes (where the chromatin fiber moves together with the solvent). Using linear response methods, we derive explicit expressions for the response functions that connect the chromatin density and velocity correlation functions to the corresponding correlation functions of the active sources and the complex viscoelastic moduli of the chromatin solution. We then derive general expressions for the flow spectral density of the chromatin velocity field. We use the theory to analyze experimental results recently obtained by one of the present authors and her co-workers. We find that the time dependence of the experimental data for both native and ATP-depleted chromatin can be well-fitted using a simple model—the Maxwell fluid—for the complex modulus, although there is some discrepancy in terms of the wavevector dependence. Thermal fluctuations of ATP-depleted cells are predominantly longitudinal. ATP-active cells exhibit intense transverse long wavelength velocity fluctuations driven by force dipoles. Fluctuations with wavenumbers larger than a few inverse microns are dominated by concentration fluctuations with the same spectrum as thermal fluctuations but with increased intensity.     

Perspective: Time scales in scientific research with an emphasis on microbial cellular and molecular research

Scientists use time to describe and research the universe in which humans live. Geologists and evolutionary biologists often use time scales in the millions to billions of years while biochemists and molecular biologists use time scales in the milliseconds or less. The atom smashers use time scales that are almost the speed of light. However, in some areas of research such as molecular-based activities in cells, it is very challenging to obtain data sets in molecular time scales. This has been a challenge to obtaining accurate and precise measurements at the cell and molecular levels of organization in living organisms. Measurements of specific cellular and molecular activities are often made over time scales longer than the actual molecular events. The data sets obtained become estimates over seconds, minutes and hours and not measurements over milli- and nanoseconds. The question can then be posed — how representative and accurate are our data sets when the time scales are not synchronized with the actual living events? In this article, the role of time scales in scientific research and our understanding of living microorganisms are examined with an emphasis on cell and molecular time scales.     

Machine vision based stochastic analysis of cancer cell mitochondrial dysfunction induced by a BH3 domain

We have developed a versatile and rapid method for the quantitative estimation of cell death kinetics, following direct single-shot activation of the mitochondrial death pathway by a cell permeable BH3 activator peptide (D-R₈BH3^BID). This approach employs timelapse epifluorescent imaging of live cells and a machine- vision based feature extraction algorithm, to measure unidirectional stochastic transitions associated with mitochondrial inner membrane potential depolarization and/or permeability transition, at single cell resolution. This data is transformed to enable construction of a right step-wise survival function using the product limit estimator, and estimation of a median latency parameter (λ), defined for the entire imaged cell population. Estimates of λ computed for cells exhibiting two-colour fluorescence can be compared statistically using the Mantel-Hansel test. This general method has been applied to measure the kinetics and temporal ordering of BH3 domain induced mitochondrial depolarization and inner membrane permeabilization in cancer cells, and demonstrates the robustness of this technique in resolving temporally distinct intracellular events within individual cells.     

Reconciling taxonomy and phylogenetic inference: formalism and algorithms for describing discord and inferring taxonomic roots

Background

Understanding the evolution of biological networks can provide insight into how their modular structure arises and how they are affected by environmental changes. One approach to studying the evolution of these networks is to reconstruct plausible common ancestors of present-day networks, allowing us to analyze how the topological properties change over time and to posit mechanisms that drive the networks?? evolution. Further, putative ancestral networks can be used to help solve other difficult problems in computational biology, such as network alignment.

Results

We introduce a combinatorial framework for encoding network histories, and we give a fast procedure that, given a set of gene duplication histories, in practice finds network histories with close to the minimum number of interaction gain or loss events to explain the observed present-day networks. In contrast to previous studies, our method does not require knowing the relative ordering of unrelated duplication events. Results on simulated histories and real biological networks both suggest that common ancestral networks can be accurately reconstructed using this parsimony approach. A software package implementing our method is available under the Apache 2.0 license at http://cbcb.umd.edu/kingsford-group/parana.

Conclusions

Our parsimony-based approach to ancestral network reconstruction is both efficient and accurate. We show that considering a larger set of potential ancestral interactions by not assuming a relative ordering of unrelated duplication events can lead to improved ancestral network inference.     

Reconstructing the temporal ordering of biological samples using microarray data

MOTIVATION: Accurate time series for biological processes are difficult to estimate due to problems of synchronization, temporal sampling and rate heterogeneity. Methods are needed that can utilize multi-dimensional data, such as those resulting from DNA microarray experiments, in order to reconstruct time series from unordered or poorly ordered sets of observations. RESULTS: We present a set of algorithms for estimating temporal orderings from unordered sets of sample elements. The techniques we describe are based on modifications of a minimum-spanning tree calculated from a weighted, undirected graph. We demonstrate the efficacy of our approach by applying these techniques to an artificial data set as well as several gene expression data sets derived from DNA microarray experiments. In addition to estimating orderings, the techniques we describe also provide useful heuristics for assessing relevant properties of sample datasets such as noise and sampling intensity, and we show how a data structure called a PQ-tree can be used to represent uncertainty in a reconstructed ordering. AVAILABILITY: Academic implementations of the ordering algorithms are available as source code (in the programming language Python) on our web site, along with documentation on their use. The artificial 'jelly roll' data set upon which the algorithm was tested is also available from this web site. The publicly available gene expression data may be found at http://genome-www.stanford.edu/cellcycle/ and http://caulobacter.stanford.edu/CellCycle/.     

On the discriminability of hROIs, human visually selected regions-of-interest

Many studies have tried to answer an important question: is it possible to predict human visually selected regions-of-interest (hROIs)? hROIs are defined as the loci of eye fixations and they can be analyzed by their spatial distribution over the visual stimulus and their temporal ordering. We used a simplified set of geometrical spatial kernels and linear filter models as bottom-up conspicuity operators that produce algorithmically selected regions-of-interest, aROIs. As a direct approach we measured the ability of these aROIs to predict human scanpaths. The level of prediction is measured by two similarity indices: S _p for spatial similarity and S _s for temporal ordering similarity. At the same time we assessed the discriminability of the hROI loci, in terms of conspicuity, with respect to non-selected (not of interest) regions of an image. We prove that this discrimination is possible and further correlates with the positional similarity index S _p . Other human scanpath experimental conditions are presented in parsing diagrams and discussed. A general top–down/bottom–up scanpath model is finally formulated.     

Modeling parasitism rate and parasitism risk: an illustration using a colonially nesting songbird, the red-winged blackbird Agelaius phoeniceus

Ornithologists interested in the drivers of nest success and brood parasitism benefit from the development of new analytical approaches. One example is the development of so-called "log exposure" models for analyzing nest success. However, analyses of brood parasitism data have not kept pace with developments in nest success analyses. The standard approach uses logistic regression which does not account for multiple parasitism events, nor does it prevent bias from using observed proportions of parasitized nests. Likewise, logistic regression analyses do not capture fine scale temporal variation in parasitism. At first glance, it might be tempting to apply log exposure models to parasitism data, but the process of parasitism is inherently different from the process of nest predation. We modeled daily parasitism rate as a Poisson process, which allowed us to correct potential biases in parasitism rate. We were also able to use our estimated parasitism rate to model parasitism risk as the probability of one or more parasitism events. We applied this model to red-winged blackbird Agelaius phoeniceus nesting colonies subject to parasitism by brown-headed cowbirds Molothrus ater . Our approach allowed us to model parasitism using a wider rage of covariates, especially functions of time. We found strong support for models combining temporal fluctuations in parasitism rate and nest-site characteristics. Similarly, we found that our annual predicted parasitism risk was lower on average than the risk estimated from observed parasitism levels. Our approach improves upon traditional logistic regression analyses and opens the door for more mechanistic modeling of the process of parasitism.     

A quantitative model for ordered Cdk substrate dephosphorylation during mitotic exit

After sister chromatid splitting at anaphase onset, exit from mitosis comprises an ordered series of events. Dephosphorylation of numerous mitotic substrates, which were phosphorylated by cyclin-dependent kinase (Cdk), is thought to bring about mitotic exit, but how temporal ordering of mitotic exit events is achieved is poorly understood. Here, we show, using budding yeast, that dephosphorylation of Cdk substrates involved in sequential mitotic exit events occurs with ordered timing. We test different models of how ordering might be achieved by modulating Cdk and Cdk-counteracting phosphatase Cdc14 activities in vivo, as well as by kinetic analysis of Cdk substrate phosphorylation and dephosphorylation in vitro. Our results suggest that the gradual change of the phosphatase to kinase ratio over the course of mitotic exit is read out by Cdk substrates that respond by dephosphorylation at distinct thresholds. This provides an example and a mechanistic explanation for a quantitative model of cell-cycle progression.     

Exploiting the full power of temporal gene expression profiling through a new statistical test: Application to the analysis of muscular dystrophy data

Background  

The identification of biologically interesting genes in a temporal expression profiling dataset is challenging and complicated by high levels of experimental noise. Most statistical methods used in the literature do not fully exploit the temporal ordering in the dataset and are not suited to the case where temporal profiles are measured for a number of different biological conditions. We present a statistical test that makes explicit use of the temporal order in the data by fitting polynomial functions to the temporal profile of each gene and for each biological condition. A Hotelling T ²-statistic is derived to detect the genes for which the parameters of these polynomials are significantly different from each other.     

Detection and estimation of the increasing trend of cancer incidence in relatively small populations

BackgroundDetection and estimation of trends in cancer incidence rates are commonly achieved by fitting standardized rates to a joinpoint log-linear regression. The efficiency of this approach is inadequate when applied to a relatively low levels of incidence. We compared that approach with the Cuscore test with respect to detecting a log-linear increasing trend of chronic myelomonocytic leukemia (CMML) in datasets simulated to match a province of about 700,000 inhabitants.MethodsFor better efficiency, we replaced the standardized rate as the dependent variable with a continuous statistic that reflects the inverse of the standardized incidence ratio (SIR). Both procedures were applied to datasets simulated to match published results in the Girona Province of Spain. We also present the use of the q-interval in displaying the temporal pattern of the events. This approach is demonstrated by analyses of CMML diagnoses in Girona County (1994–2008).ResultsThe Cuscore was clearly more efficient than regression in detecting the simulated trend. The relative efficiency of the Cuscore is likely to be maintained in even higher levels of incidence. The use of graphical displays in providing clues regarding interpretation of the results is demonstrated.ConclusionsThe Cuscore test coupled with visual inspection of the temporal pattern of the events seems to be more efficient than regression analysis in detecting and interpreting data suspected to be at elevated risk. A confirmatory analysis is expected to weed out 75% of the superfluous significant results.     

Temporal expression of cell cycle-related proteins during spermatogenesis: establishing a timeline for onset of the meiotic divisions

During spermatogenesis, the complex events of the first meiotic prophase and division phase bring about dramatic changes in nuclear organization. One factor frustrating mechanistic dissection of these events is lack of knowledge about precisely what events occur, in what order they occur, and how they may be interrelated by temporal sequence; in other words, a precise timeline is lacking. This temporal ordering problem can be tackled by following expression and localization in mouse spermatocytes of proteins critical to events of the meiotic cell division process. These include ones that are primarily chromosomal and related to pairing and recombination, as well as kinases and substrates that mediate the cell cycle transition. Distinct and protein-specific patterns occur with respect to expression and localization throughout meiotic prophase and division and dramatic relocalization of proteins occurs as spermatocytes enter the meiotic division phase. This information provides a foundation for a meiotic timeline that can be augmented to provide, eventually, a complete catalog of meiotic events and their temporal sequence. Such a framework can clarify mechanisms of normal meiosis as well as mutant phenotypes and aberrations of the meiotic process that lead to aneuploidy.