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BackgroundNon-small cell lung cancer (NSCLC) is the most common type of lung cancer, and the median overall survival is approximately 2-3 years among patients with stage III disease. Furthermore, it is one of the deadliest types of cancer globally due to non-specific symptoms and the lack of a biomarker for early detection. The most important decision that clinicians need to make after a lung cancer diagnosis is the selection of a treatment schedule. This decision is based on, among others factors, the risk of developing metastasis.MethodsA cohort of 115 NSCLC patients treated using chemotherapy and radiotherapy with curative intent was retrospectively collated and included patients for whom positron emission tomogra-phy/computed tomography (PET/CT) images, acquired before radiotherapy, were available. The PET/CT images were used to compute radiomic features extracted from a region of interest, the primary tumor. Radiomic and clinical features were then classified to stratify the patients into short and long time to metastasis, and regression analysis was used to predict the risk of metastasis.ResultsClassification based on binarized metastasis-free survival (MFS) was applied with moderate success. Indeed, an accuracy of 0.73 was obtained for the selection of features based on the Wilcoxon test and logistic regression model. However, the Cox regression model for metastasis risk prediction performed very well, with a concordance index (c-index) score equal to 0.84.ConclusionsIt is possible to accurately predict the risk of metastasis in NSCLC patients based on radiomic features. The results demonstrate the potential use of features extracted from cancer imaging in predicting the risk of metastasis.

Since the very beginning of the COVID-19 pandemic, control policies and restrictions have been the hope for containing the rapid spread of the virus. However, the psychological and economic toll they take on society entails the necessity to develop an optimal control strategy. Assessment of the effectiveness of these interventions aided with mathematical modelling remains a non-trivial issue in terms of numerical conditioning due to the high number of parameters to estimate from a highly noisy dataset and significant correlations between policy timings. We propose a solution to the problem of parameter non-estimability utilizing data from a set of European countries. Treating a subset of parameters as common for all countries and the rest as country-specific, we construct a set of individualized models incorporating 13 different pandemic control measures, and estimate their parameters without prior assumptions. We demonstrate high predictive abilities of these models on an independent validation set and rank the policies by their effectiveness in reducing transmission rates. We show that raising awareness through information campaigns, providing income support, closing schools and workplaces, cancelling public events, and maintaining an open testing policy have the highest potential to mitigate the pandemic.

A synergy between two therapeutic agents occurs when the effect of using both is greater than the sum of the effects of using each of them separately. There are several methods of detecting synergies in the literature, but they do not take into account the relationship between the times in which the factors act. In the article, we propose and justify the use of second-order sensitivity analysis as a potential tool for the detection and visualization of this type of synergy. We test and illustrate the proposed approach using four exemplary models of combined radio-chemotherapy of cancer.

UVA radiation, which accounts for about 95% of the solar spectrum, contributes to and may be the etiological factor of skin cancers of which malignant melanoma is the most aggressive. UVA causes oxidative stress in various types of cells in the skin, keratinocyte, melanocytes, and fibroblasts, which is responsible for its cytotoxic effect. Here we used a transwell system to explore how the responses of melanoma cells to a low dose of UVA (20 kJ/m2, ~ 10% of the minimal erythema dose) are influenced by neighboring co-cultured melanoma cells or fibroblasts. This dose had a low toxicity for melanoma cells, but after irradiation, co-culture with non-irradiated melanoma cells caused a strong decline in their viability and an increased frequency of apoptosis, whereas co-culture with fibroblast exerted a protective effect on irradiated melanoma cells. At the same time, the presence of non-irradiated cells, especially fibroblasts, decreased the level of UVA-induced reactive oxygen and nitrogen species. Interleukins efficiently produced by fibroblasts seem to be main players in these effects. Our studies reveal that coexistence of fibroblasts with melanoma cells may strongly modulate the direct action and may change bystander effects exerted by UVA light. Similar modulation of the effect of UVA on melanoma cells in vivo by bystander-like signaling from neighboring cells would have consequences for the development of malignant melanoma.

We summarize results of our research studies on models of combined anticancer radio- and chemotherapy and their comparison with real clinical data. We use two mathematical techniques, which, to our knowledge, have not been applied simultaneously: optimal control theory and survival analysis. We recall results of analytical optimization of combined chemo-radio-therapy for a simple model of tumor growth with respect to the order, in which these two modes of treatment should be applied. Then we study both structural and parametric sensitivity of this model and related optimal control problem. Afterwards, we present results of survival analysis based on the Kaplan-Meier curves for different protocols of chemo-radio-therapy and compare them with real clinical data and results of optimal treatment protocols.

Mathematical models of biological processes are usually continuous time (CT) and take the form of non-linear ordinary differential equations. On the other hand the estimation of model parameters is done based on discrete time (DT), relatively rare, measurements. Hence, overall problem of parameter estimation has hybrid, continuous-discrete form: it uses CT model and minimise DT performance index depending on DT prediction errors. In our previous works we have published Generalized Back Propagation Through Time (GBPPT) method—a method allowing us to use the adjoint sensitivity analysis for obtained hybrid system, and giving as a result a computationally effective recipe for calculating gradient of the performance index in parameter space. GBPTT specifies rules for construction of the adjoint system, in particular it specifies how to manage elements interfacing between CT and DT parts of the system: ideal sampler (IS) and ideal pulser (IP). Such rules for isolated IS and IP elements has been proposed without strict formal rationale. In this article we deliver a proof of correctness of such rules. Additionally, as an illustration, we present an example of application of GBPTT to parameter estimation of chemical enzymatic reaction which is one of basic biochemical reaction.

The paper presents a novel approach to the prediction of the combined therapy outcome for non-small lung cancer patients. A hybrid model is proposed, consisting of two parts. The first one is a mathematical model of tumor response to therapy, whose parameters are expressed as linear function of data from massspectrometry of patient blood plasma samples. These linear functions constitute thesecond component of the hybrid model. A comparison of clinical and simulation-based survival curves is used to evaluate the quality of the model.

Modern multi-omics studies introduce a major challenge for biomedical data storage, processing and integration. The ability to utilize multiple different measurement techniques in order to provide a comprehensive view on the studied processes is becoming a standard in molecular biology and medicine, increasing the need for the development of new strategies used for handling various types of data in a single environment. To address this need we developed a remotely accessible BioTest platform which allows to process multi-omics data, obtained using various measurement techniques, including next-generation sequencing (NGS), oligonucleotide microarrays, and mass spectrometry. This allows to process various biomedical data from genomic level, trough transcriptomics, up to the proteomic level on a scalable environment that can handle even the largest datasets. Integrated version control for library files and intermediate results as well as the possibility of designing workflows comprised of various algorithms, ensures that all of the results are highly reproducible. Incorporated support for MapReduce jobs and Big Data processing on a high performance computer cluster allows to test multiple various hypotheses at the same time.

In this work, we consider a simple mathematical model of radiochemotherapy which includes a term responsible for radiosensitization. We focus on finding theoretically optimal controls which maximise tumour cure probability for a finite, fixed therapeutic horizon. We prove that the optimal controls for both therapies are of 0-bang type, a result which is not altered by the inclusion of the radiosensilization term. By means of numerical simulations, we show that optimal control offers a moderate increase in survival time over a sequential treatment. We then revisit in more detail a question of measuring the synergy between the therapies by means of isobolograms, a common experimental technique for measuring the additivity of two treatments.

We investigate a spatial model of growth of a tumor and its sensitivity to radiotherapy. It is assumed that the radiation dose may vary in time and space, like in intensity modulated radiotherapy (IMRT). The change of the final state of the tumor depends on local differences in the radiation dose and varies with the time and the place of these local changes. This leads to the concept of a tumor's spatiotemporal sensitivity to radiation, which is a function of time and space. We show how adjoint sensitivity analysis may be applied to calculate the spatiotemporal sensitivity of the finite difference scheme resulting from the partial differential equation describing the tumor growth. We demonstrate results of this approach to the tumor proliferation, invasion and response to radiotherapy (PIRT) model and we compare the accuracy and the computational effort of the method to the simple forward finite difference sensitivity analysis. Furthermore, we use the spatiotemporal sensitivity during the gradient-based optimization of the spatiotemporal radiation protocol and present results for different parameters of the model.

The primary diagnosis of thyroid tumors based on histopathological patterns can be ambiguous in some cases, so proper classification of thyroid diseases might be improved if molecular biomarkers support cytological and histological assessment. In this work, tissue microarrays representative for major types of thyroid malignancies—papillary thyroid cancer (classical and follicular variant), follicular thyroid cancer, anaplastic thyroid cancer, and medullary thyroid cancer—and benign thyroid follicular adenoma and normal thyroid were analyzed by mass spectrometry imaging (MSI), and then different computation approaches were implemented to test the suitability of the registered profiles of tryptic peptides for tumor classification. Molecular similarity among all seven types of thyroid specimens was estimated, and multicomponent classifiers were built for sample classification using individual MSI spectra that corresponded to small clusters of cells. Moreover, MSI components showing the most significant differences in abundance between the compared types of tissues detected and their putative identity were established by annotation with fragments of proteins identified by liquid chromatography-tandem mass spectrometry in corresponding tissue lysates. In general, high accuracy of sample classification was associated with low inter-tissue similarity index and a high number of components with significant differences in abundance between the tissues. Particularly, high molecular similarity was noted between three types of tumors with follicular morphology (adenoma, follicular cancer, and follicular variant of papillary cancer), whose differentiation represented the major classification problem in our dataset. However, low level of the intra-tissue heterogeneity increased the accuracy of classification despite high inter-tissue similarity (which was exemplified by normal thyroid and benign adenoma). We compared classifiers based on all detected MSI components (n = 1536) and the subset of the most abundant components (n = 147). Despite relatively higher contribution of components with significantly different abundance and lower overall inter-tissue similarity in the latter case, the precision of classification was generally higher using all MSI components. Moreover, the classification model based on individual spectra (a single-pixel approach) outperformed the model based on mean spectra of tissue cores. Our result confirmed the high feasibility of MSI-based approaches to multi-class detection of cancer types and proved the good performance of sample classification based on individual spectra (molecular image pixels) that overcame problems related to small amounts of heterogeneous material, which limit the applicability of classical proteomics.

Molecular mechanisms of distant metastases (M1) in papillary thyroid cancer (PTC) are poorly understood. We attempted to analyze the gene expression profile in PTC primary tumors to seek the genes associated with M1 status and characterize their molecular function. One hundred and twenty-three patients, including 36 M1 cases, were subjected to transcriptome oligonucleotide microarray analyses: (set A&mdash, U133, set B&mdash, HG 1.0 ST) at transcript and gene group level (limma, gene set enrichment analysis (GSEA)). An additional independent set of 63 PTCs, including 9 M1 cases, was used to validate results by qPCR. The analysis on dataset A detected eleven transcripts showing significant differences in expression between metastatic and non-metastatic PTC. These genes were validated on microarray dataset B. The differential expression was positively confirmed for only two genes: IGFBP3, (most significant) and ECM1. However, when analyzed on an independent dataset by qPCR, the IGFBP3 gene showed no differences in expression. Gene group analysis showed differences mainly among immune-related transcripts, indicating the potential influence of tumor immune infiltration or signal within the primary tumor. The differences in gene expression profile between metastatic and non-metastatic PTC, if they exist, are subtle and potentially detectable only in large datasets.

Background Rapid changes in the expression of many messenger RNA (mRNA) species follow exposure of cells to ionizing radiation. One of the hypothetical mechanisms of this response may include microRNA (miRNA) regulation, since the amounts of miRNAs in cells also vary upon irradiation. To address this possibility, we designed experiments using cancer-derived cell lines transfected with luciferase reporter gene containing sequences targeted by different miRNA species in its 3′- untranslated region. We focus on the early time-course response (1 h past irradiation) to eliminate secondary mRNA expression waves. Results Experiments revealed that the irradiation-induced changes in the mRNA expression depend on the miRNAs which interact with mRNA. To identify the strongest interactions, we propose a mathematical model which predicts the mRNA fold expression changes, caused by perturbation of microRNA-mRNA interactions. Model was applied to experimental data including various cell lines, irradiation doses and observation times, both ours and literature-based. Comparison of modelled and experimental mRNA expression levels given miRNA level changes allows estimating how many and which miRNAs play a significant role in transcriptome response to stress conditions in different cell types. As an example, in the human melanoma cell line the comparison suggests that, globally, a major part of the irradiation-induced changes of mRNA expression can be explained by perturbed miRNA-mRNA interactions. A subset of about 30 out of a few hundred miRNAs expressed in these cells appears to account for the changes. These miRNAs play crucial roles in regulatory mechanisms observed after irradiation. In addition, these miRNAs have a higher average content of GC and a higher number of targeted transcripts, and many have been reported to play a role in the development of cancer. Conclusions Our proposed mathematical modeling approach may be used to identify miRNAs which participate in responses of cells to ionizing radiation, and other stress factors such as extremes of temperature, exposure to toxins, and drugs. Electronic supplementary material The online version of this article (10.1186/s12864-019-5464-0) contains supplementary material, which is available to authorized users.

Despite the increasing amount of available gene expression data, integrative analysis is still hindered by its high susceptibility to microenvironment fluctuations, resulting in inter-experiment variability known as batch effects. Therefore the development of data integration strategy is now more necessary than ever. Although several normalization algorithms have already been proposed, we believe that an effective model must rely on data migration between schemes. In this paper we apply this approach to a set of microarray data from core needle biopsy of breast cancers spanning different microarray platforms, and demonstrate its effectiveness in data preparation for unsupervised analysis and multiclass classification tasks. We propose a custom tool dedicated to defining the model structure. Additionally, we compare several pipelines of data processing, combining data normalization with different batch effect correction methods.

Currently, development in high-throughput technologies generate large amount of molecular biology data at awesome rate. How to merge the mass amount of data coming from different sources to obtain significant and complementary high-level knowledge is a state-of-the-art interest in statistics, machine learning and bioinformatics communities. In this article we compare two different data fusion strategies in the context of biomedical data classification using a novel graphical interface of tool for a large-scale data classification system called SPICY. Our classification system allows to compare in controlled environment different fusion strategies for multiple feature selection methods. The results show that properly chosen fusion strategy increases the overall accuracy rate in all tested cases independently of used selection method.

In this study optimal control framework is applied to two models of radiochemotherapy. A base, simple model adopts a classical log-kill hypothesis for chemotherapy and a linear-quadratic response for radiotherapy. The model is represented by the first order nonlinear differential equations with two control variables which can be transformed into a linear differential equations with a nonlinear control action. The multi-input optimal control problem formulated for this model is solved explicitly. It is shown that optimal treatment should apply radiotherapy first, while the onset of chemotherapy should be delayed. The second model takes into account the effects of drug metabolism (pharmacokinetics) and DNA repair of adjacent strand breaks. By obtaining full analytical results for chemotherapy control and partial results for radiotherapy it is shown that an introduction of these additional processes alters the structure of optimal control, which sometimes leads to opposite conclusions. A numerical example is provided which suggests that in practice the differences may not be as critical as the purely theoretical results would suggest.

One of the important steps of analysis of any mathematical model is the sensitivity analysis. The most frequently used type of sensitivity analysis is the local parametric sensitivity analysis that answers the question how changes of model’s parameters influence the solution of the model. It is routinely used but it can be applied only for constant parameters. It cannot be applied for non-stationary parameters nor for varying in time external input signals. The full information about the sensitivity in such a case can be given by the sensitivity analysis using Green’s function. This work describes a toolbox written in MATLAB environment, which can be useful in sensitivity analysis of biomedical models described by system of ordinary differential equations. To illustrate this type of sensitivity analysis, we use the created tool to analyze a model of cell signaling pathway of p53 protein, which plays crucial role in the response of tumor and healthy cells to radiotherapy.

One of the important data mining method in biomedical research is classification task. Recent advances in biomedicine provide opportunities for molecular biology, such as measurement of activity of thousands of molecular tissue biomarkers. For example we can use data of gene expression measured by DNA microarrays or RNA-Seq technique, DNA methylation levels measured by DNA methylation microarrays or protein and phosphoprotein levels measured by reverse phase protein array. A big problem in applying large-scale genomic and proteomic data for classification problem is the dimension of these data. In this work, we propose novel multiclass feature selection and classification system for merged data from different molecular biomedical techniques. However, when we merge these data the biggest problem is the huge number of features with a limited number of samples. For that reason the feature selection step is crucial in high dimension data classification problem. Our results have shown that integrated analysis with proper feature selection and classification techniques used for large-scale meta-data can improve the classification accuracy and feature selection stability index. We have proofed, that for merged data we observe significantly higher classification accuracy for the same number of selected features as for single technique dataset.

Radiation-induced bystander effect, appearing as different biological changes in cells that are not directly exposed to ionizing radiation but are under the influence of molecular signals secreted by irradiated neighbors, have recently attracted considerable interest due to their possible implication for radiotherapy. However, various cells present diverse radiosensitivity and bystander responses that depend, inter alia, on genetic status including TP53, the gene controlling the cell cycle, DNA repair and apoptosis. Here we compared the ionizing radiation and bystander responses of human colorectal carcinoma HCT116 cells with wild type or knockout TP53 using a transwell co-culture system. The viability of exposed to X-rays (0–8 Gy) and bystander cells of both lines showed a roughly comparable decline with increasing dose. The frequency of micronuclei was also comparable at lower doses but at higher increased considerably, especially in bystander TP53-/- cells. Moreover, the TP53-/- cells showed a significantly elevated frequency of apoptosis, while TP53+/+ counterparts expressed high level of senescence. The cross-matched experiments where irradiated cells of one line were co-cultured with non-irradiated cells of opposite line show that both cell lines were also able to induce bystander effects in their counterparts, however different endpoints revealed with different strength. Potential mediators of bystander effects, IL-6 and IL-8, were also generated differently in both lines. The knockout cells secreted IL-6 at lower doses whereas wild type cells only at higher doses. Secretion of IL-8 by TP53−/− control cells was many times lower than that by TP53+/+ but increased significantly after irradiation. Transcription of the NFκBIA was induced in irradiated TP53+/+ mainly, but in bystanders a higher level was observed in TP53−/− cells, suggesting that TP53 is required for induction of NFκB pathway after irradiation but another mechanism of activation must operate in bystander cells.

Cancer results from genetic aberrations that affect multiple intracellular processes, combined with evolution and clonal selection that give cancer a significant advantage over heathy cells. Identification of genes and processes that function improperly in cancer cells is a significant challenge, necessary for the proper understanding of cancerogenesis and for the development of successful treatment scenarios. This paper shows the advantages of utilizing data provided by various methods to complement the knowledge about alterations in regulatory processes associated with cancer. Using four different experiment types that focus on mutations and indels, gene expression, copy number variation and methylation, used to study the genome of over 2000 patients treated for breast, thyroid and prostate cancer, we test some of the assumptions used in cancer research associated with coverage and mutual exclusivity of alterations. We show that individual methods do not allow to observe alterations in all cancer related processes and that the exclusivity assumption is valid only for individual alteration types. We additionally show the relationship between the violation of those assumptions and clinical data, at the level of individual patients, providing a comprehensive description of the analysis strategy used and its possible impact on the interpretation of data.

This paper describes a classification system which uses feature selection method based on logistic regression algorithm. As a feature elimination criterion the variance inflation factor of the statistical logistic regression model is used. The experimental results show that this method can be successfully applied for feature selection in classification problem of multidimensional microarray data.

This article presents a method for sensitivity analysis of non-linear continuous-time models with delays and its application to parameter estimation. The method is universal and may be used for sensitivity analysis of any system given as a block diagram with arbitrary structure and any number of delays. The method gives sensitivity functions of model trajectories with respect to all model parameters, including delay times, and both forward and adjoint sensitivity analysis may be performed. Two examples application of the method are presented: identification of a Wiener model with delay and identification of a model of JAK-STAT cell signal transduction mechanism.

In this work we present SPICY (SPecialized Classification sYstem) application for a supervised data analysis (feature selection, classification, model validation and model selection) with the structure preventing the data processing work-flow from so called information leak. The information leak may result in optimistically biased classification quality assessment, especially for large-scale, small-sample data sets. The application uses the Galaxy Server environment that originally allows the user to manual data processing and is not prevented from the information leak. The way how the classification model is built by the user and the specific structure of all implemented methods makes the information leak impossible. The lack of information leak in the presented supervised data analysis tool is demonstrated on numerical examples, where synthetic and real data sets are used.

The work presents a gradient-based approach to estimation of initial functions of time delay elements appearing in models of dynamical systems. It is shown how to generate the gradient of the estimation objective function in the initial function space using adjoint sensitivity analysis. It is assumed that the system is continuous-time and described by ordinary differential equations with delays but the estimation is done based on discrete-time measurements of the signals appearing in the system. Results of gradient-based estimation of initial functions for exemplary models are presented and discussed.

Planning identification experiments for cell signaling pathways: An NFκB case studyMathematical modeling of cell signaling pathways has become a very important and challenging problem in recent years. The importance comes from possible applications of obtained models. It may help us to understand phenomena appearing in single cells and cell populations on a molecular level. Furthermore, it may help us with the discovery of new drug therapies. Mathematical models of cell signaling pathways take different forms. The most popular way of mathematical modeling is to use a set of nonlinear ordinary differential equations (ODEs). It is very difficult to obtain a proper model. There are many hypotheses about the structure of the model (sets of variables and phenomena) that should be verified. The next step, fitting the parameters of the model, is also very complicated because of the nature of measurements. The blotting technique usually gives only semi-quantitative observations, which are very noisy and collected only at a limited number of time moments. The accuracy of parameter estimation may be significantly improved by a proper experiment design. Recently, we have proposed a gradient-based algorithm for the optimization of a sampling schedule. In this paper we use the algorithm in order to optimize a sampling schedule for the identification of the mathematical model of the NFκB regulatory module, known from the literature. We propose a two-stage optimization approach: a gradient-based procedure to find all stationary points and then pair-wise replacement for finding optimal numbers of replicates of measurements. Convergence properties of the presented algorithm are examined.

Age-structured models describe heterogeneous populations of individuals. Life of the individual consist of a finite number of phases, which differ in properties such as the ability to reproduce. This approach allows more realistic modelling of the population growth than using models assuming homogeneity of the population, which is especially important for complex organisms with long reproduction time. The aim of this study was to develop a methodology to estimate parameters of the age-structured model of cell cycle using adjoint sensitivity analysis. Results were obtained for artificially generated input data.

Low birth weight is an important factor of the health of an infant because of being a major determinant of morbidity, disability, and mortality during infancy and childhood. Low birth weight is a multifaceted public health problem. The prevalence of this diagnosis is estimated to be 15–20 % worldwide (more than 20 million infants) and occurs mostly in developing countries (95.6 %). There are many factors, which affect the birth weight of newborns. From a medical point of view, it is important to find out, which factors are important and determine the risk of not normal birth weight. In this work, we propose to use the classification system to find out which features are important to classify the neonates into birth weight groups. In presented approach, we use different classification and feature selection methods to analyze a new questionnaire-based obstetric data set. Our results show that a small number of features is enough to achieve high classification accuracy rate and the set of selected features is significant from biological and medical point of view.

There are many impediments to progress in cancer research. Insufficient or low quality data and computational tools that are dispersed among various sites are one of them. In this paper we present an integrated system that combines all stages of cancer studies, from gathering of clinical data, through elaborate patient questionnaires and bioinformatics tools, to data warehousing and preparation of analysis reports.

Testing biomedical hypotheses is performed based on advanced and usually many-step analysis of biomedical data. This requires sophisticated analytical methods and data structures that allow to store intermediate results, which are needed in the subsequent steps. However, biomedical data, especially reference data, often change in time and new analytical methods are created every year. This causes the necessity to repeat the iterative analyses with new methods and new reference data sets, which in turn causes frequent changes of the underlying data structures. Such instability of data structures can be mitigated by the use of the idea of data lake, instead of traditional database systems.

The paper concerns the problem of fitting mathematical models of cell signaling pathways. Such models frequently take the form of sets of nonlinear ordinary differential equations. While the model is continuous in time, the performance index used in the fitting procedure involves measurements taken at discrete time moments. Adjoint sensitivity analysis is a tool which can be used for finding the gradient of a performance index in the space of parameters of the model. In the paper, a structural formulation of adjoint sensitivity analysis called the generalized backpropagation through time (GBPTT) is used. The method is especially suited for hybrid, continuous-discrete time systems. As an example, we use the mathematical model NF-kappaB of the regulatory module, which plays a major role in the innate immune response in animals.

DNA microarray technology is the latest and the most advanced tool for parallel measuring of the activity and interactions of thousands of genes. This modern technology promises new insight into mechanisms of living systems, for example only two high-density oligonucleotide microarrays are sufficient to inspect the whole human genome. However, it provides unprecedented amount of data that require application of advanced computational methods. The appropriate choice of data analysis technique depends both on data and on goals of an experiment. In this paper we focus on two promising methods: singular value decomposition and support vector machines. We discuss the possibility of application of these methods for different purposes; particularly for clustering, classification, feature selection and modeling of dynamics of gene expression. We use for testing presented approaches existing data sets, which are widely available via Internet, and one new tumor/normal thyroid microarray data set.

Microarrays provide a new technique of measuring gene expression that attracted a lot of research interest in recent years. It has been suggested that gene expression data from microarrays (biochips) can be utilized in many biomedical areas, for example in cancer classification. Whereas several, new and existing, methods of classification has been tested, a selection of proper (optimal) set of genes, which expression serves during classification, is still an open problem. In this paper we propose a heuristic method of choosing suboptimal set of genes by using support vector machines (SVM). Obtained set of genes optimizes leave-one-out cross-validation error. The method is tested on microarray gene expression data of samples of two cancer types: acute myeloid leukemia (AML) and acute lymphoblastic leukemia (ALL). The results show that quality of classification is much better than for sets obtained using other methods of feature selection. In addition, we demonstrate that maximum separation in a training data set may lead to deterioration of performance in an independent validation data set, a phenomenon akin to overfitting.

The detection of somatic mutations in indeterminate or follicular proliferation fine-needle aspiration cytologies (FNACs) is able to clarify only a subgroup of those FNACs. Therefore, further markers to differentiate this problematic FNAC category by the identification of mutation negative thyroid cancers and benign nodules are urgently needed. Our objective was to evaluate previously published miRNA markers and discover novel ones from all publicly available miRNA expression profiling data sets. By literature review and data repository search we gathered 3 data sets describing human miRNA expression profiles of follicular thyroid cancer (FTC) and follicular adenoma (FA) samples. Literature review summarized 27 previously published miRNAs, which were validated in the 3 available data sets. By means of uniform statistical analysis 6 further miRNAs were identified and tested in an independent, previously published microarray data set. Meta-analysis confirmed 7 out of 27 previously published, and 4 out of 6 de novo identified miRNAs. The low confirmation rate of previously published miRNA markers was induced by low numbers of samples in the analyzed studies and high false discovery rates that were higher than 0.2. Finally, miR-637, miR-181c-3p, miR-206, and miR-7-5p were discovered as de novo potential FTC markers and validated in at least one independent, previously published data set. Two out of these new identified miRNAs (miR-7-5p and miR-206) were validated by qPCR in an independent sample set of 32 FTC and 46 FA samples. Especially miR-7-5p was able to differentiate benign and malignant thyroid tumors in several datasets.

A problem of parameter estimation for non-linear models may be solved using different approaches, but in general cases it can be always transformed to an optimization problem. In such a case the minimized objective function is a measure of the discrepancy between the model solution and available measurements. This paper presents the ADFIT program — a tool for numerical parameter estimation for models that contain systems of non-linear ordinary differential equations. The user of the program provides a model in a symbolic form and the experimental data. The program utilizes adjoint sensitivity analysis to speed up gradient calculation of the quadratic objective function. The adjoint system generating the gradient is created automatically based on the symbolic form of the model. A numerical example of parameter estimation for a mathematical model arising in biology is also presented.

Recent studies indicates that cellular cancerogenesis is connected with microRNA (miRNA) expression levels. In particular, different miRNAs can serve as classification features for distinguishing different cancer types. This paper provides classification attempt using miRNA isoforms with 3’-end modification as classification features. microRNA samples was obtained using next generation sequencing method. Data was preprocessed using authors algorithm developed in R. Support Vector Mashines and Partial Least Square methods were used to classify two types of miRNA samples: Follicular Adenoma and Follicular Thyroid Cancer. It was observed that only several miRNA modified isoforms were identified as the most differentiating for analyzed samples. Obtained results indicate that miRNA 3’-end modifications can be used as cancer tissue classification features.

The problem of feature selection for large-scale genomic data, for example from DNA microarray experiments, is one of the fundamental and well-investigated problems in modern computational biology. From the computational point of view, a selected gene list should be characterized by good predictive power and should be understood and well explained from the biological point of view. Recently, another feature of selected gene lists is increasingly investigated, namely their stability which measures how the content and/or the gene order change when the data are perturbed. In this paper we propose a new approach to analysis of gene list stability, termed the sensitivity index, that does not require any data perturbation and allows the gene list that is most reliable in a biological sense to be chosen.

This paper concerns the problem of fitting of mathematical models of cell signaling pathways. Such models frequently take the form of a set of nonlinear ordinary differential equations. While the model is continuous-time, the performance index, used in the fitting procedure, involves measurements taken only at discrete-time moments. Adjoint sensitivity analysis is a tool that can be used for finding a gradient of a performance index in the space of the model’s parameters. The paper uses a structural formulation of sensitivity analysis, especially dedicated for hybrid, continuous/discrete-time systems. A numerical example of fitting of the mathematical model of the NF-kB regulatory module is presented.

—In the paper we present a brief survey of our results in processing of data from DNA microarray experiments obtained in our collaborative research with M.C. Sklodowska Centre of Oncology. Our experience therefore is strictly connected with problems resulting from cancer diagnosis and therapy but many results have more general issue. We focus our attention on three important stages of microarray data processing e.g. class prediction, gene selection and pattern discovery.

Selection of novel molecular markers is an important goal of cancer genomics studies. The aim of our analysis was to apply the multivariate bioinformatical tools to rank the genes – potential markers of papillary thyroid cancer (PTC) according to their diagnostic usefulness. We also assessed the accuracy of benign/malignant classification, based on gene expression profiling, for PTC. We analyzed a 180-array dataset (90 HG-U95A and 90 HG-U133A oligonucleotide arrays), which included a collection of 57 PTCs, 61 benign thyroid tumors, and 62 apparently normal tissues. Gene selection was carried out by the support vector machines method with bootstrapping, which allowed us 1) ranking the genes that were most important for classification quality and appeared most frequently in the classifiers (bootstrap-based feature ranking, BBFR); 2) ranking the samples, and thus detecting cases that were most difficult to classify (bootstrap-based outlier detection). The accuracy of PTC diagnosis was 98.5% for a 20-gene classifier, its 95% confidence interval (CI) was 95.9–100%, with the lower limit of CI exceeding 95% already for five genes. Only 5 of 180 samples (2.8%) were misclassified in more than 10% of bootstrap iterations. We specified 43 genes which are most suitable as molecular markers of PTC, among them some well-known PTC markers (MET, fibronectin 1, dipeptidylpeptidase 4, or adenosine A1 receptor) and potential new ones (UDP-galactose-4-epimerase, cadherin 16, gap junction protein 3, sushi, nidogen, and EGF-like domains 1, inhibitor of DNA binding 3, RUNX1, leiomodin 1, F-box protein 9, and tripartite motif-containing 58). The highest ranking gene, metallophosphoesterase domain-containing protein 2, achieved 96.7% of the maximum BBFR score.

Medullary thyroid carcinoma occurs both as a sporadic and a familial disease. Inherited MTC (iMTC) patients usually exhibit better prognosis than patients with sporadic form of MTC (sMTC), however, in both subtypes the outcome is unpredictable. No molecular markers contributing to the prognosis or predicting the type of therapy have been introduced to clinical practice until now. The aim of this study was to analyze gene expression pattern of MTC by high density oligonucleotide microarray.24 samples were studied: 12 MTC and 12 corresponding normal tissues, (Affymetrix HG-U 133A). Among MTC patients there were half inherited cases and half sporadic ones.First, the differences between MTC and thyroid tissue were analyzed by Singular Value Decomposition (SVD) which indicated three main modes determining the variability of gene expression profile: the first two were related to the tumor/normal tissue difference and the third one was related to the immune response. The characteristic expression pattern, beside of numerous changes within cancer- related genes, included many up-regulated genes specific for thyroid C cells. Further analysis of the second component revealed two subgroups of MTC, but the subdivision was not related to the iMTC/sMTC difference. Recursive Feature Replacement (RFR) confirmed the very similar expression profile in both forms of MTC. With subsequent ANOVA analysis some genes with differential expression could be specified, among them monoamine oxidase B (MAOB) and gamma-aminobutyric acid receptor (GABRR1) which were consistently up-regulated in sMTC. In contrary, some genes involved in regulation of cell proliferation: opioid growth factor receptor(OGFR) and synaptotagmin V (SYT 5) were up-regulated in iMTC.The obtained data indicate a very similar gene expression pattern in inherited and sporadic MTC. Minor differences in their molecular profile require further analysis.

There are an increasing number of studies analyzing gene expression profiles in various benign and malignant thyroid tumors. This creates the opportunity to validate results obtained from one microarray study with those from other data sets. This process requires rigorous methods for accurate comparison.The ability to compare data sets derived from different Affymetrix GeneChip generations and the influence of intra- and interindividual comparisons of gene expression data were evaluated to build multigene classifiers of benign thyroid nodules to verify a previously proposed papillary thyroid carcinoma (PTC) classifier and to look for molecular pathways essential for PTC oncogenesis.Gene expression profile data sets from autonomously functioning and cold thyroid nodules and from PTC were analyzed by support vector machines. GenMAPP analysis was used for PTC data analysis to examine the expression patterns of biologically relevant gene sets.Only intraindividual reference samples allowed the identification of subtle changes in the expression patterns of relevant signaling cascades, such as the MAPK pathway in PTC. Using an artificial intelligence approach, the autonomously functioning and cold thyroid nodule multigene classifiers were derived and evaluated by cross-comparisons.We recommend defining classifiers within one generation of gene chips and subsequently checking them across different array generations. Using this approach, we have demonstrated the specificity of a previously reported PTC classifier on an independent collection of benign tumors. Moreover, we propose multigene classifiers for different types of benign thyroid nodules.

The study looked for an optimal set of genes differentiating between papillary thyroid cancer (PTC) and normal thyroid tissue and assessed the sources of variability in gene expression profiles. The analysis was done by oligonucleotide microarrays (GeneChip HG-U133A) in 50 tissue samples taken intraoperatively from 33 patients (23 PTC patients and 10 patients with other thyroid disease). In the initial group of 16 PTC and 16 normal samples, we assessed the sources of variability in the gene expression profile by singular value decomposition which specified three major patterns of variability. The first and the most distinct mode grouped transcripts differentiating between tumor and normal tissues. Two consecutive modes contained a large proportion of immunity-related genes. To generate a multigene classifier for tumor-normal difference, we used support vector machines-based technique (recursive feature replacement). It included the following 19 genes: DPP4, GJB3, ST14, SERPINA1, LRP4, MET, EVA1, SPUVE, LGALS3, HBB, MKRN2, MRC2, IGSF1, KIAA0830, RXRG, P4HA2, CDH3, IL13RA1, and MTMR4, and correctly discriminated 17 of 18 additional PTC/normal thyroid samples and all 16 samples published in a previous microarray study. Selected novel genes (LRP4, EVA1, TMPRSS4, QPCT, and SLC34A2) were confirmed by Q-PCR.Our results prove that the gene expression signal of PTC is easily detectable even when cancer cells do not prevail over tumor stroma. We indicate and separate the confounding variability related to the immune response. Finally, we propose a potent molecular classifier able to discriminate between PTC and nonmalignant thyroid in more than 90% of investigated samples.

This paper deals with a problem of evaluation of nonlinear model of the helicopter. The plant is an educational apparatus with two degree of freedom. Whereas the theory of linear identification is well established, there are several possible approaches to identification or evaluation of nonlinear plants. Here so called Generalized Back Propagation Through Time Method (GBPTT) is utilized. This method, derived originally for recurrent neural networks, can be used for any nonlinear dynamical system given as a block diagram. The method is fully structural and, in addition, mnemonic. The results of applying of GBPTT for the helicopter shows that obtained model outperforms the model achieved by separate measurements or estimation of its parameters.

The objective of the studies described here was the development of a mathematical model which would fit experimental data for the repair of single and double strand breaks induced in DNA in living cells by exposure to ionizing radiation, and which would allow to better understand the processes of DNA repair. DNA breaks are believed to play the major role in radiation-induced lethality and formation of chromosome deletions, and are therefore crucial to the response of cells to radiotherapy. In an initial model which we reported on the basis of data for the repair of Epstein-Barr minichromosomes in irradiated Raji cells, we assumed that DNA breaks are induced only at the moment of irradiation and are later removed by repair systems. This work gives a development of that mathematical model which fits the experimental results more precisely and suggests strongly that DNA breaks are generated not only by direct irradiation but also later, probably by systems engaged in repair of oxidative damage.

This paper deals with a problem of finding of suboptimal control law for a counterflow heat exchanger. The counterflow heat exchanger is a non-linear, multidimensional, distributed parameter system, which frequently appears in industrial and civil installations. The most common task is to control of output temperature of one medium. In previous works of the author [7, 8] the problem of identification and finding suboptimal control signal in open-loop system has been solved using so called Generalized Back Propagation Through Time (GBPTT) method [4]. In this paper in order to decrease influence of disturbances the control law will be introduced. State variables of the model, which serves as a state observer are arguments of the control law. Parameters of the control law are optimized using GBPTT method. Numerical examples are presented.