Binary Markov Random Fields and interpretable mass spectra discrimination.

For mass spectra acquired from cancer patients by MALDI or SELDI techniques, automated discrimination between cancer types or stages has often been implemented by machine learning algorithms. Nevertheless, these techniques typically lack interpretability in terms of biomarkers. In this paper, we propose a new mass spectra discrimination algorithm by parameterized Markov Random Fields to automatically generate interpretable classifiers with small groups of scored biomarkers. A dataset of 238 MALDI colorectal mass spectra and two datasets of 216 and 253 SELDI ovarian mass spectra respectively were used to test our approach. The results show that our approach reaches accuracies of 81% to 100% to discriminate between patients from different colorectal and ovarian cancer stages, and performs as well or better than previous studies on similar datasets. Moreover, our approach enables efficient planar-displays to visualize mass spectra discrimination and has good asymptotic performance for large datasets. Thus, our classifiers should facilitate the choice and planning of further experiments for biological interpretation of cancer discriminating signatures. In our experiments, the number of mass spectra for each colorectal cancer stage is roughly half of that for each ovarian cancer stage, so that we reach lower discrimination accuracy for colorectal cancer than for ovarian cancer.

Modeling delay in genetic networks: from delay birth-death processes to delay stochastic differential equations.

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

Analysis and Modeling of Early Estradiol-induced GREB1 Single Allele Gene Transcription at the Population Level.

Single molecule fluorescence in situ hybridization (smFISH) can be used to visualize transcriptional activation at the single allele level. We and others have applied this approach to better understand the mechanisms of activation by steroid nuclear receptors. However, there is limited understanding of the interconnection between the activation of target gene alleles inside the same nucleus and within large cell populations. Using the GREB1 gene as an early estrogen receptor (ER) response target, we applied smFISH to track E2-activated GREB1 allelic transcription over early time points to evaluate potential dependencies between alleles within the same nucleus. We compared two types of experiments where we altered the initial status of GREB1 basal transcription by treating cells with and without the elongation inhibitor flavopiridol (FV). E2 stimulation changed the frequencies of active GREB1 alleles in the cell population independently of FV pre-treatment. In FV treated cells, the response time to hormone was delayed, albeit still reaching at 90 minutes the same levels as in cells not treated by FV. We show that the joint frequencies of GREB1 activated alleles observed at the cell population level imply significant dependency between pairs of alleles within the same nucleus. We identify probabilistic models of joint alleles activations by applying a principle of maximum entropy. For pairs of alleles, we have then quantified statistical dependency by computing their mutual information. We have then introduced a stochastic model compatible with allelic statistical dependencies, and we have fitted this model to our data by intensive simulations. This provided estimates of the average lifetime for degradation of GREB1 introns and of the mean time between two successive transcription rounds. Our approach informs on how to extract information on single allele regulation by ER from within a large population of cells, and should be applicable to many other genes. AUTHOR SUMMARY: After application of a gene transcription stimulus, in this case the hormone 17 ß -estradiol, on large populations of cells over a short time period, we focused on quantifying and modeling the frequencies of GREB1 single allele activations. We have established an experimental and computational pipeline to analyze large numbers of high resolution smFISH images to detect and monitor active GREB1 alleles, that can be translatable to any target gene of interest. A key result is that, at the population level, activation of individual GREB1 alleles within the same nucleus do exhibit statistically significant dependencies which we quantify by the mutual information between activation states of pairs of alleles. After noticing that frequencies of joint alleles activations observed over our large cell populations evolve smoothly in time, we have defined a population level stochastic model which we fit to the observed time course of GREB1 activation frequencies. This provided coherent estimates of the mean time between rounds of GREB1 transcription and the mean lifetime of nascent mRNAs. Our algorithmic approach and experimental methods are applicable to many other genes.

Estimation of the rate and effect of new beneficial mutations in asexual populations.

The rate and effect of available beneficial mutations are key parameters in determining how a population adapts to a new environment. However, these parameters are poorly known, in large part because of the difficulty of designing and interpreting experiments to examine the rare and intrinsically stochastic process of mutation occurrence. We present a new approach to estimate the rate and selective advantage of beneficial mutations that underlie the adaptation of asexual populations. We base our approach on the analysis of experiments that track the effect of newly arising beneficial mutations on the dynamics of a neutral marker in evolving bacterial populations and develop efficient estimators of mutation rate and selective advantage. Using extensive simulations, we evaluate the accuracy of our estimators and conclude that they are quite robust to the use of relatively low experimental replication. To validate the predictions of our model, we compare theoretical and experimentally determined estimates of the selective advantage of the first beneficial mutation to fix in a series of ten replicate populations. We find that our theoretical predictions are not significantly different from experimentally determined selection coefficients. Application of our method to suitably designed experiments will allow estimation of how population evolvability depends on demographic and initial fitness parameters.

Valve Strain Quantitation in Normal Mitral Valves and Mitral Prolapse With Variable Degrees of Regurgitation.

OBJECTIVES: The aim of this study was to quantitate patient-specific mitral valve (MV) strain in normal valves and in patients with mitral valve prolapse with and without significant mitral regurgitation (MR) and assess the determinants of MV strain. BACKGROUND: Few data exist on MV deformation during systole in humans. Three-dimensional echocardiography allows for dynamic MV imaging, enabling digital modeling of MV function in health and disease. METHODS: Three-dimensional transesophageal echocardiography was performed in 82 patients, 32 with normal MV and 50 with mitral valve prolapse (MVP): 12 with mild mitral regurgitation or less (MVP - MR) and 38 with moderate MR or greater (MVP + MR). Three-dimensional MV models were generated, and the peak systolic strain of MV leaflets was computed on proprietary software. RESULTS: Left ventricular ejection fraction was normal in all groups. MV annular dimensions were largest in MVP + MR (annular area: 13.8 ± 0.7 cm2) and comparable in MVP - MR (10.6 ± 1 cm2) and normal valves (10.5 ± 0.3 cm2; analysis of variance: p < 0.001). Similarly, MV leaflet areas were largest in MVP + MR, particularly the posterior leaflet (8.7 ± 0.5 cm2); intermediate in MVP - MR (6.5 ± 0.7 cm2); and smallest in normal valves (5.5 ± 0.2 cm2; p < 0.0001). Strain was overall highest in MVP + MR and lowest in normal valves. Patients with MVP - MR had intermediate strain values that were higher than normal valves in the posterior leaflet (p = 0.001). On multivariable analysis, after adjustment for clinical and MV geometric parameters, leaflet thickness was the only parameter that was retained as being significantly correlated with mean MV strain (r = 0.34; p = 0.008). CONCLUSIONS: MVs that exhibit prolapse have higher strain compared to normal valves, particularly in the posterior leaflet. Although higher strain is observed with worsening MR and larger valves and annuli, mitral valve leaflet thickness-and, thus, underlying MV pathology-is the most significant independent determinant of valve deformation. Future studies are needed to assess the impact of MV strain determination on clinical outcome.

Mitral Valve Remodeling and Strain in Secondary Mitral Regurgitation: Comparison With Primary Regurgitation and Normal Valves.

OBJECTIVES: The aim of this study was to assess mitral valve (MV) remodeling and strain in patients with secondary mitral regurgitation (SMR) compared with primary MR (PMR) and normal valves. BACKGROUND: A paucity of data exists on MV strain during the cardiac cycle in humans. Real-time 3-dimensional (3D) echocardiography allows for dynamic MV imaging, enabling computerized modeling of MV function in normal and disease states. METHODS: Three-dimensional transesophageal echocardiography (TEE) was performed in a total of 106 subjects: 36 with SMR, 38 with PMR, and 32 with normal valves; MR severity was at least moderate in both MR groups. Valve geometric parameters were quantitated and patient-specific 3D MV models generated in systole using a dedicated software. Global and regional peak systolic MV strain was computed using a proprietary software. RESULTS: MV annular area was larger in both the SMR and PMR groups (12.7 ± 0.7 and 13.3 ± 0.7 cm2, respectively) compared with normal subjects (9.9 ± 0.3 cm2; p < 0.05). The leaflets also had significant remodeling, with total MV leaflet area larger in both SMR (16.2 ± 0.9 cm2) and PMR (15.6 ± 0.8 cm2) versus normal subjects (11.6 ± 0.4 cm2). Leaflets in SMR were thicker than those in normal subjects but slightly less than those with PMR posteriorly. Posterior leaflet strain was significantly higher than anterior leaflet strain in all 3 groups. Despite MV remodeling, strain in SMR (8.8 ± 0.3%) was overall similar to normal subjects (8.5 ± 0.2%), and both were lower than in PMR (12 ± 0.4%; p < 0.0001). Valve thickness, severity of MR, and primary etiology of MR were correlates of strain, with leaflet thickness being the multivariable parameter significantly associated with MV strain. In patients with less severe MR, anterior leaflet strain in SMR was lower than normal, whereas strain in PMR remained higher than normal. CONCLUSIONS: The MV in secondary MR remodels significantly and similarly to PMR with a resultant larger annular area, leaflet surface area, and leaflet thickness compared with that of normal subjects. Despite these changes, MV strain remains close to or in some instances lower than normal and is significantly lower than that of PMR. Strain determination has the potential to improve characterization of MV mechano-biologic properties in humans and to evaluate its prognostic impact in patients with MR, with or without valve interventions.

Localization of epileptic seizure focus by computerized analysis of fMRI recordings.

By computerized analysis of cortical activity recorded via fMRI for pediatric epilepsy patients, we implement algorithmic localization of epileptic seizure focus within one of eight cortical lobes. Our innovative machine learning techniques involve intensive analysis of large matrices of mutual information coefficients between pairs of anatomically identified cortical regions. Drastic selection of pairs of regions with biologically significant inter-connectivity provides efficient inputs for our multi-layer perceptron (MLP) classifier. By imposing rigorous parameter parsimony to avoid overfitting, we construct a small-size MLP with very good percentages of successful classification.

Mutual Information Better Quantifies Brain Network Architecture in Children with Epilepsy.

PURPOSE: Metrics of the brain network architecture derived from resting-state fMRI have been shown to provide physiologically meaningful markers of IQ in children with epilepsy. However, traditional measures of functional connectivity (FC), specifically the Pearson correlation, assume a dominant linear relationship between BOLD time courses; this assumption may not be valid. Mutual information is an alternative measure of FC which has shown promise in the study of complex networks due to its ability to flexibly capture association of diverse forms. We aimed to compare network metrics derived from mutual information-defined FC to those derived from traditional correlation in terms of their capacity to predict patient-level IQ. MATERIALS AND METHODS: Patients were retrospectively identified with the following: (1) focal epilepsy; (2) resting-state fMRI; and (3) full-scale IQ by a neuropsychologist. Brain network nodes were defined by anatomic parcellation. Parcellation was performed at the size threshold of 350 mm2, resulting in networks containing 780 nodes. Whole-brain, weighted graphs were then constructed according to the pairwise connectivity between nodes. In the traditional condition, edges (connections) between each pair of nodes were defined as the absolute value of the Pearson correlation coefficient between their BOLD time courses. In the mutual information condition, edges were defined as the mutual information between time courses. The following metrics were then calculated for each weighted graph: clustering coefficient, modularity, characteristic path length, and global efficiency. A machine learning algorithm was used to predict the IQ of each individual based on their network metrics. Prediction accuracy was assessed as the fractional variation explained for each condition. RESULTS: Twenty-four patients met the inclusion criteria (age: 8-18 years). All brain networks demonstrated expected small-world properties. Network metrics derived from mutual information-defined FC significantly outperformed the use of the Pearson correlation. Specifically, fractional variation explained was 49% (95% CI: 46%, 51%) for the mutual information method; the Pearson correlation demonstrated a variation of 17% (95% CI: 13%, 19%). CONCLUSION: Mutual information-defined functional connectivity captures physiologically relevant features of the brain network better than correlation. CLINICAL RELEVANCE: Optimizing the capacity to predict cognitive phenotypes at the patient level is a necessary step toward the clinical utility of network-based biomarkers.

Patient-Specific Quantitation of Mitral Valve Strain by Computer Analysis of Three-Dimensional Echocardiography: A Pilot Study.

BACKGROUND: A paucity of data exists on mitral valve (MV) deformation during the cardiac cycle in man. Real-time 3-dimensional (3D) echocardiography now allows dynamic volumetric imaging of the MV, thus enabling computerized modeling of MV function directly in health and disease. METHODS AND RESULTS: MV imaging using 3D transesophageal echocardiography was performed in 10 normal subjects and 10 patients with moderate-to-severe or severe organic mitral regurgitation. Using proprietary 3D software, patient-specific models of the mitral annulus and leaflets were computed at mid- and end-systole. Strain analysis of leaflet deformation was derived from these models. In normals, mean strain intensity averaged 0.11±0.02 and was higher in the posterior leaflet than in the anterior leaflet (0.13±0.03 versus 0.10±0.02; P<0.05). Mean strain intensity was higher in patients with mitral regurgitation (0.15±0.03) than in normals (0.11±0.02; P=0.05). Higher mean strain intensity was noted for the posterior leaflet in both normal and organic valves. Regional valve analysis revealed that both anterior and posterior leaflets have the highest strain concentration in the commissural zone, and the boundary zone near the annulus and at the coaptation line, with reduced strain concentration in the central leaflet zone. CONCLUSIONS: In normals, MV strain is higher in the posterior leaflet, with the highest strain at the commissures, annulus, and coaptation zones. Patients with organic mitral regurgitation have higher strain than normals. Three-dimensional echocardiography allows noninvasive and patient-specific quantitation of strain intensities because of MV deformations and has the potential to improve noninvasive characterization and follow-up of MV disease.

Robust Selection Algorithm (RSA) for Multi-Omic Biomarker Discovery; Integration with Functional Network Analysis to Identify miRNA Regulated Pathways in Multiple Cancers.

MicroRNAs (miRNAs) play a crucial role in the maintenance of cellular homeostasis by regulating the expression of their target genes. As such, the dysregulation of miRNA expression has been frequently linked to cancer. With rapidly accumulating molecular data linked to patient outcome, the need for identification of robust multi-omic molecular markers is critical in order to provide clinical impact. While previous bioinformatic tools have been developed to identify potential biomarkers in cancer, these methods do not allow for rapid classification of oncogenes versus tumor suppressors taking into account robust differential expression, cutoffs, p-values and non-normality of the data. Here, we propose a methodology, Robust Selection Algorithm (RSA) that addresses these important problems in big data omics analysis. The robustness of the survival analysis is ensured by identification of optimal cutoff values of omics expression, strengthened by p-value computed through intensive random resampling taking into account any non-normality in the data and integration into multi-omic functional networks. Here we have analyzed pan-cancer miRNA patient data to identify functional pathways involved in cancer progression that are associated with selected miRNA identified by RSA. Our approach demonstrates the way in which existing survival analysis techniques can be integrated with a functional network analysis framework to efficiently identify promising biomarkers and novel therapeutic candidates across diseases.

Genome-wide perturbations by miRNAs map onto functional cellular pathways, identifying regulators of chromatin modifiers.

BACKGROUND: Regulation of gene expression by microRNAs (miRNAs) is critical for determining cellular fate and function. Dysregulation of miRNA expression contributes to the development and progression of multiple diseases. miRNA can target multiple mRNAs, making deconvolution of the effects of miRNA challenging and the complexity of regulation of cellular pathways by miRNAs at the functional protein level remains to be elucidated. Therefore, we sought to determine the effects of expression of miRNAs in breast and ovarian cancer cells on cellular pathways by measuring systems-wide miRNA perturbations to protein and phosphoproteins. METHODS: We measure protein level changes by reverse-phase protein array (RPPA) in MDA-MB-231, SKOV3.ip1 and HEYA8 cancer cell lines transfected by a library of 879 human miRNA mimics. RESULTS: The effects of multiple miRNAs-protein networks converged in five broad functional clusters of miRNA, suggesting a broad overlap of miRNA action on cellular pathways. Detailed analysis of miRNA clusters revealed novel miRNA/cell cycle protein networks, which we functionally validated. De novo phosphoprotein network estimation using Gaussian graphical modeling, using no priors, revealed known and novel protein interplay, which we also observed in patient ovarian tumor proteomic data. We identified several miRNAs that have pluripotent activities across multiple cellular pathways. In particular we studied miR-365a whose expression is associated with poor survival across several cancer types and demonstrated that anti-miR-365 significantly reduced tumor formation in animal models. CONCLUSIONS: Mapping of miRNA-induced protein and phosphoprotein changes onto pathways revealed new miRNA-cellular pathway connectivity, paving the way for targeting of dysregulated pathways with potential miRNA-based therapeutics.

Modeling miRNA-mRNA interactions: fitting chemical kinetics equations to microarray data.

BACKGROUND: The miRNAs are small non-coding RNAs of roughly 22 nucleotides in length, which can bind with and inhibit protein coding mRNAs through complementary base pairing. By degrading mRNAs and repressing proteins, miRNAs regulate the cell signaling and cell functions. This paper focuses on innovative mathematical techniques to model gene interactions by algorithmic analysis of microarray data. Our goal was to elucidate which mRNAs were actually degraded or had their translation inhibited by miRNAs belonging to a very large pool of potential miRNAs. RESULTS: We proposed two chemical kinetics equations (CKEs) to model the interactions between miRNAs, mRNAs and the associated proteins. In order to reduce computational cost, we used a non linear profile clustering method named minimal net clustering and efficiently condensed the large set of expression profiles observed in our microarray data sets. We determined unknown parameters of the CKE models by minimizing the discrepancy between model prediction and data, using our own fast non linear optimization algorithm. We then retained only the CKE models for which the optimized fit to microarray data is of high quality and validated multiple miRNA-mRNA pairs. CONCLUSION: The implementation of CKE modeling and minimal net clustering reduces drastically the potential set of miRNA-mRNA pairs, with a high gain for further experimental validations. The minimal net clustering also provides good miRNA candidates that have similar regulatory roles.

Impact of miRNA sequence on miRNA expression and correlation between miRNA expression and cell cycle regulation in breast cancer cells.

The miRNAs regulate cell functions by inhibiting expression of proteins. Research on miRNAs had usually focused on identifying targets by base pairing between miRNAs and their targets. Instead of identifying targets, this paper proposed an innovative approach, namely impact significance analysis, to study the correlation between mature sequence, expression across patient samples or time and global function on cell cycle signaling of miRNAs. With three distinct types of data: The Cancer Genome Atlas miRNA expression data for 354 human breast cancer specimens, microarray of 266 miRNAs in mouse Embryonic Stem cells (ESCs), and Reverse Phase Protein Array (RPPA) transfected by 776 miRNAs in MDA-MB-231 cell line, we linked the expression and function of miRNAs by their mature sequence and discovered systematically that the similarity of miRNA expression enhances the similarity of miRNA function, which indicates the miRNA expression can be used as a supplementary factor to predict miRNA function. The results also show that both seed region and 3' portion are associated with miRNA expression levels across human breast cancer specimens and in ESCs; miRNAs with similar seed tend to have similar 3' portion. And we discussed that the impact of 3' portion, including nucleotides 13-16, is not significant for miRNA function. These results provide novel insights to understand the correlation between miRNA sequence, expression and function. They can be applied to improve the prediction algorithm and the impact significance analysis can also be implemented to similar analysis for other small RNAs such as siRNAs.

Mapping network motif tunability and robustness in the design of synthetic signaling circuits.

Cellular networks are highly dynamic in their function, yet evolutionarily conserved in their core network motifs or topologies. Understanding functional tunability and robustness of network motifs to small perturbations in function and structure is vital to our ability to synthesize controllable circuits. In establishing core sets of network motifs, we selected topologies that are overrepresented in mammalian networks, including the linear, feedback, feed-forward, and bifan circuits. Static and dynamic tunability of network motifs were defined as the motif ability to respectively attain steady-state or transient outputs in response to pre-defined input stimuli. Detailed computational analysis suggested that static tunability is insensitive to the circuit topology, since all of the motifs displayed similar ability to attain predefined steady-state outputs in response to constant inputs. Dynamic tunability, in contrast, was tightly dependent on circuit topology, with some motifs performing superiorly in achieving observed time-course outputs. Finally, we mapped dynamic tunability onto motif topologies to determine robustness of motif structures to changes in topology and identify design principles for the rational assembly of robust synthetic networks.

Biomarker Signature Discovery from Mass Spectrometry Data.

Mass spectrometry based high throughput proteomics are used for protein analysis and clinical diagnosis. Many machine learning methods have been used to construct classifiers based on mass spectrometry data, for discrimination between cancer stages. However, the classifiers generated by machine learning such as SVM techniques typically lack biological interpretability. We present an innovative technique for automated discovery of signatures optimized to characterize various cancer stages. We validate our signature discovery algorithm on one new colorectal cancer MALDI-TOF data set, and two well-known ovarian cancer SELDI-TOF data sets. In all of these cases, our signature based classifiers performed either better or at least as well as four benchmark machine learning algorithms including SVM and KNN. Moreover, our optimized signatures automatically select smaller sets of key biomarkers than the black-boxes generated by machine learning, and are much easier to interpret.

Rigid-motion-invariant classification of 3-D textures.

This paper studies the problem of 3-D rigid-motion-invariant texture discrimination for discrete 3-D textures that are spatially homogeneous by modeling them as stationary Gaussian random fields. The latter property and our formulation of a 3-D rigid motion of a texture reduce the problem to the study of 3-D rotations of discrete textures. We formally develop the concept of 3-D texture rotations in the 3-D digital domain. We use this novel concept to define a "distance" between 3-D textures that remains invariant under all 3-D rigid motions of the texture. This concept of "distance" can be used for a monoscale or a multiscale 3-D rigid-motion-invariant testing of the statistical similarity of the 3-D textures. To compute the "distance" between any two rotations R(1) and R(2) of two given 3-D textures, we use the Kullback-Leibler divergence between 3-D Gaussian Markov random fields fitted to the rotated texture data. Then, the 3-D rigid-motion-invariant texture distance is the integral average, with respect to the Haar measure of the group SO(3), of all of these divergences when rotations R(1) and R(2) vary throughout SO(3). We also present an algorithm enabling the computation of the proposed 3-D rigid-motion-invariant texture distance as well as rules for 3-D rigid-motion-invariant texture discrimination/classification and experimental results demonstrating the capabilities of the proposed 3-D rigid-motion texture discrimination rules when applied in a multiscale setting, even on very general 3-D texture models.

miRNA regulatory circuits in ES cells differentiation: a chemical kinetics modeling approach.

MicroRNAs (miRNAs) play an important role in gene regulation for Embryonic Stem cells (ES cells), where they either down-regulate target mRNA genes by degradation or repress protein expression of these mRNA genes by inhibiting translation. Well known tables TargetScan and miRanda may predict quite long lists of potential miRNAs inhibitors for each mRNA gene, and one of our goals was to strongly narrow down the list of mRNA targets potentially repressed by a known large list of 400 miRNAs. Our paper focuses on algorithmic analysis of ES cells microarray data to reliably detect repressive interactions between miRNAs and mRNAs. We model, by chemical kinetics equations, the interaction architectures implementing the two basic silencing processes of miRNAs, namely "direct degradation" or "translation inhibition" of targeted mRNAs. For each pair (M,G) of potentially interacting miRMA gene M and mRNA gene G, we parameterize our associated kinetic equations by optimizing their fit with microarray data. When this fit is high enough, we validate the pair (M,G) as a highly probable repressive interaction. This approach leads to the computation of a highly selective and drastically reduced list of repressive pairs (M,G) involved in ES cells differentiation.