Accurate state estimation from uncertain data and models: an application of data assimilation to mathematical models of human brain tumors

Background

Data assimilation refers to methods for updating the state vector (initial condition) of a complex spatiotemporal model (such as a numerical weather model) by combining new observations with one or more prior forecasts. We consider the potential feasibility of this approach for making short-term (60-day) forecasts of the growth and spread of a malignant brain cancer (glioblastoma multiforme) in individual patient cases, where the observations are synthetic magnetic resonance images of a hypothetical tumor.

Results

We apply a modern state estimation algorithm (the Local Ensemble Transform Kalman Filter), previously developed for numerical weather prediction, to two different mathematical models of glioblastoma, taking into account likely errors in model parameters and measurement uncertainties in magnetic resonance imaging. The filter can accurately shadow the growth of a representative synthetic tumor for 360 days (six 60-day forecast/update cycles) in the presence of a moderate degree of systematic model error and measurement noise.

Conclusions

The mathematical methodology described here may prove useful for other modeling efforts in biology and oncology. An accurate forecast system for glioblastoma may prove useful in clinical settings for treatment planning and patient counseling.

Reviewers

This article was reviewed by Anthony Almudevar, Tomas Radivoyevitch, and Kristin Swanson (nominated by Georg Luebeck).     

Pregnancy outcomes in women with repeated implantation failures after intracytoplasmic morphologically selected sperm injection (IMSI)

Background

The role of serum anti-Müllerian hormone (AMH) as predictor of in-vitro fertilization outcomes has been much debated. The aim of the present study is to investigate the practicability of combining serum AMH level with biological age as a simple screening method for counseling IVF candidates of advanced reproductive age with potential poor outcomes prior to treatment initiation.

Methods

A total of 1,538 reference patients and 116 infertile patients aged greater than or equal to 40 years enrolled in IVF/ICSI cycles were recruited in this retrospective analysis. A reference chart of the age-related distribution of serum AMH level for Asian population was first created. IVF/ICSI patients aged greater than or equal to 40 years were then divided into three groups according to the low, middle and high tertiles the serum AMH tertiles derived from the reference population of matching age. The cycle outcomes were analyzed and compared among each individual group.

Results

For reference subjects aged greater than or equal to 40 years, the serum AMH of the low, middle and high tertiles were equal or lesser than 0.48, 0.49-1.22 and equal or greater than 1.23 ng/mL respectively. IVF/ICSI patients aged greater than or equal to 40 years with AMH levels in the low tertile had the highest cycle cancellation rate (47.6%) with zero clinical pregnancy. The nadir AMH level that has achieved live birth was 0.56 ng/mL, which was equivalent to the 36.4th percentile of AMH level from the age-matched reference group. The optimum cut-off levels of AMH for the prediction of nonpregnancy and cycle cancellation were 1.05 and 0.68 ng/mL, respectively.

Conclusions

Two criteria: (1) age greater than or equal to 40 years and (2) serum AMH level in the lowest tertile (equal or lesser than 33.3rd percentile) of the matching age group, may be used as markers of futility for counseling IVF/ICSI candidates.     

Interplay between soil drying and root exudation in rhizosheath development

Background and Aims

Wetting-drying cycles are important environmental processes known to enhance aggregation. However, very little attention has been given to drying as a process that transports mucilage to inter-particle contacts where it is deposited and serves as binding glue. The objective of this study was to formulate and test conceptual and mathematical models that describe the role of drying in soil aggregation through transportation and deposition of binding agents.

Methods

We used an ESEM to visualize aggregate formation of pair of glass beads. To test our model, we subjected three different sizes of sand to multiple wetting-drying cycles of PGA solution as a mimic of root exudates to form artificial aggregates. Water stable aggregate was determined using wet sieving apparatus.

Results

A model to predict aggregate stability in presence of organic matter was developed, where aggregate stability depends on soil texture as well as the strength, density and mass fraction of organic matter, which was confirmed experimentally. The ESEM images emphasize the role of wetting-drying cycles on soil aggregate formation.

Conclusions

Our experimental results confirmed the mathematical model predictions as well as the ESEM images on the role of drying in soil aggregation as an agent for transport and deposition of binding agents.     

Swift block-updating EM and pseudo-EM procedures for Bayesian shrinkage analysis of quantitative trait loci

Introduction

Virtually all existing expectation-maximization (EM) algorithms for quantitative trait locus (QTL) mapping overlook the covariance structure of genetic effects, even though this information can help enhance the robustness of model-based inferences.

Results

Here, we propose fast EM and pseudo-EM-based procedures for Bayesian shrinkage analysis of QTLs, designed to accommodate the posterior covariance structure of genetic effects through a block-updating scheme. That is, updating all genetic effects simultaneously through many cycles of iterations.

Conclusion

Simulation results based on computer-generated and real-world marker data demonstrated the ability of our method to swiftly produce sensible results regarding the phenotype-to-genotype association. Our new method provides a robust and remarkably fast alternative to full Bayesian estimation in high-dimensional models where the computational burden associated with Markov chain Monte Carlo simulation is often unwieldy. The R code used to fit the model to the data is provided in the online supplementary material.     

Improving prediction of burial state of residues by exploiting correlation among residues

Background

Residues in a protein might be buried inside or exposed to the solvent surrounding the protein. The buried residues usually form hydrophobic cores to maintain the structural integrity of proteins while the exposed residues are tightly related to protein functions. Thus, the accurate prediction of solvent accessibility of residues will greatly facilitate our understanding of both structure and functionalities of proteins. Most of the state-of-the-art prediction approaches consider the burial state of each residue independently, thus neglecting the correlations among residues.

Results

In this study, we present a high-order conditional random field model that considers burial states of all residues in a protein simultaneously. Our approach exploits not only the correlation among adjacent residues but also the correlation among long-range residues. Experimental results showed that by exploiting the correlation among residues, our approach outperformed the state-of-the-art approaches in prediction accuracy. In-depth case studies also showed that by using the high-order statistical model, the errors committed by the bidirectional recurrent neural network and chain conditional random field models were successfully corrected.

Conclusions

Our methods enable the accurate prediction of residue burial states, which should greatly facilitate protein structure prediction and evaluation.

     

A molecular diffusion based utility model for Drosophila larval phototaxis

Background

Generally, utility based decision making models focus on experimental outcomes. In this paper we propose a utility model based on molecular diffusion to simulate the choice behavior of Drosophila larvae exposed to different light conditions.

Methods

In this paper, light/dark choice-based Drosophila larval phototaxis is analyzed with our molecular diffusion based model. An ISCEM algorithm is developed to estimate the model parameters.

Results

By applying this behavioral utility model to light intensity and phototaxis data, we show that this model fits the experimental data very well.

Conclusions

Our model provides new insights into decision making mechanisms in general. From an engineering viewpoint, we propose that the model could be applied to a wider range of decision making practices.     

ALC: automated reduction of rule-based models

Background

Combinatorial complexity is a challenging problem for the modeling of cellular signal transduction since the association of a few proteins can give rise to an enormous amount of feasible protein complexes. The layer-based approach is an approximative, but accurate method for the mathematical modeling of signaling systems with inherent combinatorial complexity. The number of variables in the simulation equations is highly reduced and the resulting dynamic models show a pronounced modularity. Layer-based modeling allows for the modeling of systems not accessible previously.

Results

ALC (Automated Layer Construction) is a computer program that highly simplifies the building of reduced modular models, according to the layer-based approach. The model is defined using a simple but powerful rule-based syntax that supports the concepts of modularity and macrostates. ALC performs consistency checks on the model definition and provides the model output in different formats (C MEX, MATLAB, Mathematica and SBML) as ready-to-run simulation files. ALC also provides additional documentation files that simplify the publication or presentation of the models. The tool can be used offline or via a form on the ALC website.

Conclusion

ALC allows for a simple rule-based generation of layer-based reduced models. The model files are given in different formats as ready-to-run simulation files.     

Integrated multi-level quality control for proteomic profiling studies using mass spectrometry

Background

Evolutionary conservation of RNA secondary structure is a typical feature of many functional non-coding RNAs. Since almost all of the available methods used for prediction and annotation of non-coding RNA genes rely on this evolutionary signature, accurate measures for structural conservation are essential.

Results

We systematically assessed the ability of various measures to detect conserved RNA structures in multiple sequence alignments. We tested three existing and eight novel strategies that are based on metrics of folding energies, metrics of single optimal structure predictions, and metrics of structure ensembles. We find that the folding energy based SCI score used in the RNAz program and a simple base-pair distance metric are by far the most accurate. The use of more complex metrics like for example tree editing does not improve performance. A variant of the SCI performed particularly well on highly conserved alignments and is thus a viable alternative when only little evolutionary information is available. Surprisingly, ensemble based methods that, in principle, could benefit from the additional information contained in sub-optimal structures, perform particularly poorly. As a general trend, we observed that methods that include a consensus structure prediction outperformed equivalent methods that only consider pairwise comparisons.

Conclusion

Structural conservation can be measured accurately with relatively simple and intuitive metrics. They have the potential to form the basis of future RNA gene finders, that face new challenges like finding lineage specific structures or detecting mis-aligned sequences.     

BioSuper: A web tool for the superimposition of biomolecules and assemblies with rotational symmetry

Background

Predicting protein structure from sequence is one of the most significant and challenging problems in bioinformatics. Numerous bioinformatics techniques and tools have been developed to tackle almost every aspect of protein structure prediction ranging from structural feature prediction, template identification and query-template alignment to structure sampling, model quality assessment, and model refinement. How to synergistically select, integrate and improve the strengths of the complementary techniques at each prediction stage and build a high-performance system is becoming a critical issue for constructing a successful, competitive protein structure predictor.

Results

Over the past several years, we have constructed a standalone protein structure prediction system MULTICOM that combines multiple sources of information and complementary methods at all five stages of the protein structure prediction process including template identification, template combination, model generation, model assessment, and model refinement. The system was blindly tested during the ninth Critical Assessment of Techniques for Protein Structure Prediction (CASP9) in 2010 and yielded very good performance. In addition to studying the overall performance on the CASP9 benchmark, we thoroughly investigated the performance and contributions of each component at each stage of prediction.

Conclusions

Our comprehensive and comparative study not only provides useful and practical insights about how to select, improve, and integrate complementary methods to build a cutting-edge protein structure prediction system but also identifies a few new sources of information that may help improve the design of a protein structure prediction system. Several components used in the MULTICOM system are available at: http://sysbio.rnet.missouri.edu/multicom_toolbox/.     

Aromatase inhibitors in post-menopausal endometriosis

Background

Serum anti-Mullerian hormone (AMH) is currently considered the best marker of ovarian reserve and of ovarian responsiveness to gonadotropins in in-vitro fertilization (IVF). AMH assay, however, is not available in all IVF Units and is quite expensive, a reason that limits its use in developing countries. The aim of this study is to assess whether the "ovarian sensitivity index" precisely reflects AMH so that this index may be used as a surrogate for AMH in prediction of ovarian response during an IVF cycle.

Methods

AMH serum levels were measured in 61 patients undergoing IVF with a "long" stimulation protocol including the GnRH agonist buserelin and recombinant follicle-stimulating hormone (rFSH). Patients were divided into four subgroups according to the percentile of serum AMH and their ovarian stimulation was prospectively followed. Ovarian sensitivity index (OSI) was calculated dividing the total administered FSH dose by the number of retrieved oocytes.

Results

AMH and OSI show a highly significant negative correlation (r = -0.67; p = 0.0001) that is stronger than the one between AMH and the total number of retrieved oocytes and than the one between AMH and the total FSH dose.

Conclusions

OSI reflects quite satisfactory the AMH level and may be proposed as a surrogate of AMH assay in predicting ovarian responsiveness to FSH in IVF. Being very easy to calculate and costless, its use could be proposed where AMH measurement is not available or in developing countries where limiting costs is of primary importance.     

WGCNA: an R package for weighted correlation network analysis

Background

Modelling the time-related behaviour of biological systems is essential for understanding their dynamic responses to perturbations. In metabolic profiling studies, the sampling rate and number of sampling points are often restricted due to experimental and biological constraints.

Results

A supervised multivariate modelling approach with the objective to model the time-related variation in the data for short and sparsely sampled time-series is described. A set of piecewise Orthogonal Projections to Latent Structures (OPLS) models are estimated, describing changes between successive time points. The individual OPLS models are linear, but the piecewise combination of several models accommodates modelling and prediction of changes which are non-linear with respect to the time course. We demonstrate the method on both simulated and metabolic profiling data, illustrating how time related changes are successfully modelled and predicted.

Conclusion

The proposed method is effective for modelling and prediction of short and multivariate time series data. A key advantage of the method is model transparency, allowing easy interpretation of time-related variation in the data. The method provides a competitive complement to commonly applied multivariate methods such as OPLS and Principal Component Analysis (PCA) for modelling and analysis of short time-series data.     

Evaluating a non-destructive method for calibrating tree biomass equations derived from tree branching architecture

Key message

Functional branch analysis (FBA) is a promising non-destructive method that can produce accurate tree biomass equations when applied to trees which exhibit fractal branching architecture.

Abstract

Functional branch analysis (FBA) is a promising non-destructive alternative to the standard destructive method of tree biomass equation development. In FBA, a theoretical model of tree branching architecture is calibrated with measurements of tree stems and branches to estimate the coefficients of the biomass equation. In this study, species-specific and mixed-species tree biomass equations were derived from destructive sampling of trees in Western Kenya and compared to tree biomass equations derived non-destructively from FBA. The results indicated that the non-destructive FBA method can produce biomass equations that are similar to, but less accurate than, those derived from standard methods. FBA biomass prediction bias was attributed to the fact that real trees diverged from fractal branching architecture due to highly variable length–diameter relationships of stems and branches and inaccurate scaling relationships for the lengths of tree crowns and trunks assumed under the FBA model.     

miREE: miRNA recognition elements ensemble

Background

The accurate prediction of ligand binding residues from amino acid sequences is important for the automated functional annotation of novel proteins. In the previous two CASP experiments, the most successful methods in the function prediction category were those which used structural superpositions of 3D models and related templates with bound ligands in order to identify putative contacting residues. However, whilst most of this prediction process can be automated, visual inspection and manual adjustments of parameters, such as the distance thresholds used for each target, have often been required to prevent over prediction. Here we describe a novel method FunFOLD, which uses an automatic approach for cluster identification and residue selection. The software provided can easily be integrated into existing fold recognition servers, requiring only a 3D model and list of templates as inputs. A simple web interface is also provided allowing access to non-expert users. The method has been benchmarked against the top servers and manual prediction groups tested at both CASP8 and CASP9.

Results

The FunFOLD method shows a significant improvement over the best available servers and is shown to be competitive with the top manual prediction groups that were tested at CASP8. The FunFOLD method is also competitive with both the top server and manual methods tested at CASP9. When tested using common subsets of targets, the predictions from FunFOLD are shown to achieve a significantly higher mean Matthews Correlation Coefficient (MCC) scores and Binding-site Distance Test (BDT) scores than all server methods that were tested at CASP8. Testing on the CASP9 set showed no statistically significant separation in performance between FunFOLD and the other top server groups tested.

Conclusions

The FunFOLD software is freely available as both a standalone package and a prediction server, providing competitive ligand binding site residue predictions for expert and non-expert users alike. The software provides a new fully automated approach for structure based function prediction using 3D models of proteins.     

Comparison of total parathyroidectomy without autotransplantation and without thymectomy versus total parathyroidectomy with autotransplantation and with thymectomy for secondary hyperparathyroidism: TOPAR PILOT-Trial

Introduction

The clinical significance of a treatment effect demonstrated in a randomized trial is typically assessed by reference to differences in event rates at the group level. An alternative is to make individualized predictions for each patient based on a prediction model. This approach is growing in popularity, particularly for cancer. Despite its intuitive advantages, it remains plausible that some prediction models may do more harm than good. Here we present a novel method for determining whether predictions from a model should be used to apply the results of a randomized trial to individual patients, as opposed to using group level results.

Methods

We propose applying the prediction model to a data set from a randomized trial and examining the results of patients for whom the treatment arm recommended by a prediction model is congruent with allocation. These results are compared with the strategy of treating all patients through use of a net benefit function that incorporates both the number of patients treated and the outcome. We examined models developed using data sets regarding adjuvant chemotherapy for colorectal cancer and Dutasteride for benign prostatic hypertrophy.

Results

For adjuvant chemotherapy, we found that patients who would opt for chemotherapy even for small risk reductions, and, conversely, those who would require a very large risk reduction, would on average be harmed by using a prediction model; those with intermediate preferences would on average benefit by allowing such information to help their decision making. Use of prediction could, at worst, lead to the equivalent of an additional death or recurrence per 143 patients; at best it could lead to the equivalent of a reduction in the number of treatments of 25% without an increase in event rates. In the Dutasteride case, where the average benefit of treatment is more modest, there is a small benefit of prediction modelling, equivalent to a reduction of one event for every 100 patients given an individualized prediction.

Conclusion

The size of the benefit associated with appropriate clinical implementation of a good prediction model is sufficient to warrant development of further models. However, care is advised in the implementation of prediction modelling, especially for patients who would opt for treatment even if it was of relatively little benefit.     

Predicting forest site productivity in temperate lowland from forest floor, soil and litterfall characteristics using boosted regression trees

Aims

The aim of this study is on the one hand to identify the most determining variables predicting the site productivity of pedunculate oak, common beech and Scots pine in temperate lowland forests of Flanders; and on the other hand to test whether the accuracy of site productivity models based exclusively on soil or forest floor predictor variables is similar to the accuracy achieved by full ecosystem models, combining all soil, vegetation, humus and litterfall composition related variables.

Methods

Boosted Regression Trees (BRT) were used to model in a climatically homogeneous region the relationship between environmental variables and site productivity. A distinction was made between soil (soil physical and chemical), forest floor (vegetation and humus) and ecosystem (soil, forest floor and litterfall composition jointly) predictors.

Results

Our results have illustrated the strength of BRT to model the non-linear behaviour of ecological processes. The ecosystem models, based on all collected variables, explained most of the variability and were more accurate than those limited to either soil or forest floor variables. Nevertheless, both the soil and forest floor models can serve as good predictive models for many forest management practices.

Conclusions

Soil granulometric fractions and litterfall nitrogen concentrations were the most effective predictors of forest site productivity in Flanders. Although many studies revealed a fertilising effect of increased nitrogen deposition, nitrogen saturation seemed to reduce species’ productivity in this region.     

Genome-based prediction of maize hybrid performance across genetic groups,testers, locations,and years

Key message

The calibration data for genomic prediction should represent the full genetic spectrum of a breeding program. Data heterogeneity is minimized by connecting data sources through highly related test units.

Abstract

One of the major challenges of genome-enabled prediction in plant breeding lies in the optimum design of the population employed in model training. With highly interconnected breeding cycles staggered in time the choice of data for model training is not straightforward. We used cross-validation and independent validation to assess the performance of genome-based prediction within and across genetic groups, testers, locations, and years. The study comprised data for 1,073 and 857 doubled haploid lines evaluated as testcrosses in 2 years. Testcrosses were phenotyped for grain dry matter yield and content and genotyped with 56,110 single nucleotide polymorphism markers. Predictive abilities strongly depended on the relatedness of the doubled haploid lines from the estimation set with those on which prediction accuracy was assessed. For scenarios with strong population heterogeneity it was advantageous to perform predictions within a priori defined genetic groups until higher connectivity through related test units was achieved. Differences between group means had a strong effect on predictive abilities obtained with both cross-validation and independent validation. Predictive abilities across subsequent cycles of selection and years were only slightly reduced compared to predictive abilities obtained with cross-validation within the same year. We conclude that the optimum data set for model training in genome-enabled prediction should represent the full genetic and environmental spectrum of the respective breeding program. Data heterogeneity can be reduced by experimental designs that maximize the connectivity between data sources by common or highly related test units.     

Optimized submerged batch fermentation strategy for systems scale studies of metabolic switching in Streptomyces coelicolor A3(2)

Background

Given the complex mechanisms underlying biochemical processes systems biology researchers tend to build ever increasing computational models. However, dealing with complex systems entails a variety of problems, e.g. difficult intuitive understanding, variety of time scales or non-identifiable parameters. Therefore, methods are needed that, at least semi-automatically, help to elucidate how the complexity of a model can be reduced such that important behavior is maintained and the predictive capacity of the model is increased. The results should be easily accessible and interpretable. In the best case such methods may also provide insight into fundamental biochemical mechanisms.

Results

We have developed a strategy based on the Computational Singular Perturbation (CSP) method which can be used to perform a "biochemically-driven" model reduction of even large and complex kinetic ODE systems. We provide an implementation of the original CSP algorithm in COPASI (a COmplex PAthway SImulator) and applied the strategy to two example models of different degree of complexity - a simple one-enzyme system and a full-scale model of yeast glycolysis.

Conclusion

The results show the usefulness of the method for model simplification purposes as well as for analyzing fundamental biochemical mechanisms. COPASI is freely available at http://www.copasi.org.     

Cluster-Rasch models for microarray gene expression data

Background

We propose two different formulations of the Rasch statistical models to the problem of relating gene expression profiles to the phenotypes. One formulation allows us to investigate whether a cluster of genes with similar expression profiles is related to the observed phenotypes; this model can also be used for future prediction. The other formulation provides an alternative way of identifying genes that are over- or underexpressed from their expression levels in tissue or cell samples of a given tissue or cell type.

Results

We illustrate the methods on available datasets of a classification of acute leukemias and of 60 cancer cell lines. For tumor classification, the results are comparable to those previously obtained. For the cancer cell lines dataset, we found four clusters of genes that are related to drug response for many of the 90 drugs that we considered. In addition, for each type of cell line, we identified genes that are over- or underexpressed relative to other genes.

Conclusions

The cluster-Rasch model provides a probabilistic model for describing gene expression patterns across samples and can be used to relate gene expression profiles to phenotypes.     

ICSI diagnostic: a way to prevent total fertilization failure after 4 unsuccessful IUI

Background

The aim of this retrospective study is to investigate the relevance of dividing oocytes and using some for traditional in vitro fertilization (IVF) and others for intracytoplasmic sperm injection (ICSI) as of the first IVF cycle in patients with unexplained infertility who have undergone 4 intrauterine insemination (IUI) cycles which produced no pregnancies.

Methods

This retrospective study includes patients with unexplained infertility who have failed to become pregnant, after 4 IUI, despite normal semen parameters after sperm capacitation. These women were treated in our assisted fertilization program from 2008 until 2015. We analysed the first cycles of women in whom more than 4 oocyte cumulus complexes (OCC) were retrieved and single embryo transfer was performed.

Results

Dividing oocytes between two fertilization techniques reduce the rate of total fertilization failure during the first IVF cycle. No statistical difference were observed for 2 pronuclei (PN) rate between the two techniques. On the other hand, we observed a significantly lower rate of 3 PN, 1 PN, 0 PN with ICSI in comparison with conventional fertilization.

Conclusions

Splitting the oocytes between classical IVF and ICSI increases the chance of embryo transfer on a first IVF cycle after 4 unsuccessful IUI cycles. This half-and-half policy reduces the risk, for the infertile couple, of facing total failure of fertilization and also can provide useful information for the next attempts.