Andrzej Polanski

Optimal control problems arising in cell‐cycle‐specific cancer chemotherapy

We explore mathematical properties of models of cancer chemotherapy including cell‐cycle dependence. Using the mathematical methods of control theory, we demonstrate two assertions of interest for the biomedical community: 1 Periodic chemotherapy protocols are close to the optimum for a wide class of models and have additional favourable properties. 2 Two possible approaches, (a) to minimize the final count of malignant cells and the cumulative effect of the drug on normal cells, or (b) to maximize the final count of normal cells and the cumulative effect of the drug on malignant cells, lead to similar principles of optimization.

Mass spectrometry-based serum proteome pattern analysis in molecular diagnostics of early stage breast cancer

BackgroundMass spectrometric analysis of the blood proteome is an emerging method of clinical proteomics. The approach exploiting multi-protein/peptide sets (fingerprints) detected by mass spectrometry that reflect overall features of a specimens proteome, termed proteome pattern analysis, have been already shown in several studies to have applicability in cancer diagnostics. We aimed to identify serum proteome patterns specific for early stage breast cancer patients using MALDI-ToF mass spectrometry.MethodsBlood samples were collected before the start of therapy in a group of 92 patients diagnosed at stages I and II of the disease, and in a group of age-matched healthy controls (104 women). Serum specimens were purified and the low-molecular-weight proteome fraction was examined using MALDI-ToF mass spectrometry after removal of albumin and other high-molecular-weight serum proteins. Protein ions registered in a mass range between 2,000 and 10,000 Da were analyzed using a new bioinformatic tool created in our group, which included modeling spectra as a sum of Gaussian bell-shaped curves.ResultsWe have identified features of serum proteome patterns that were significantly different between blood samples of healthy individuals and early stage breast cancer patients. The classifier built of three spectral components that differentiated controls and cancer patients had 83% sensitivity and 85% specificity. Spectral components (i.e., protein ions) that were the most frequent in such classifiers had approximate m/z values of 2303, 2866 and 3579 Da (a biomarker built from these three components showed 88% sensitivity and 78% specificity). Of note, we did not find a significant correlation between features of serum proteome patterns and established prognostic or predictive factors like tumor size, nodal involvement, histopathological grade, estrogen and progesterone receptor expression. In addition, we observed a significantly (p = 0.0003) increased level of osteopontin in blood of the group of cancer patients studied (however, the plasma level of osteopontin classified cancer samples with 88% sensitivity but only 28% specificity).ConclusionMALDI-ToF spectrometry of serum has an obvious potential to differentiate samples between early breast cancer patients and healthy controls. Importantly, a classifier built on MS-based serum proteome patterns outperforms available protein biomarkers analyzed in blood by immunoassays.

Molecular mechanisms of autosomal recessive hypercholesterolemia.

Purpose of review Autosomal recessive hypercholesterolemia (ARH) is a rare Mendelian dyslipidemia characterized by markedly elevated plasma LDL levels, xanthomatosis, and premature coronary artery disease. LDL receptor function is normal, or only moderately impaired in fibroblasts from ARH patients, but their cultured lymphocytes show increased cell-surface LDL binding, and impaired LDL degradation, consistent with a defect in LDL receptor internalization. Recently, the disorder was shown to be caused by mutations in a phosphotyrosine binding domain protein, ARH, which is required for internalization of low density lipoproteins in the liver. This review summarizes the findings of new investigations into the pathophysiology and molecular genetics of ARH. Recent findings All mutations that have been characterized to date preclude the synthesis of a full-length protein. GST-pulldown experiments indicate that the phosphotyrosine binding domain of ARH interacts with the internalization sequence (NPVY) in the cytoplasmic tail of LDLR, and that conserved motifs in the C-terminal portion of the protein bind to clathrin and to the β2-adaptin subunit of AP-2. Summary The available data suggest that ARH functions as an adaptor protein that couples LDLR to the endocytic machinery.

Lyapunov function construction by linear programming

In this paper the Lyapunov function given by the infinity norm is considered. A new proof of the theorem of Molchanov and Pyatintskii (1986) is given, The presented proof enables us to give an explicit calculation of the matrix which was only demonstrated to exist in the original paper. Combining the obtained result with the idea of scaling faces of a polytope gives the method of fitting the shape of level surfaces, of the Lyapunov function given by the infinity norm, to the specified demands.

A note on distributions of times to coalescence, under time-dependent population size

Expressions for marginal distributions of times in the time-varying coalescence process are derived. The proposed method allows also for computation of joint probability distribution for pairs, triples, etc. of coalescence times. The expressions derived are useful for (1) extending several statistics from time constant to time-varying case, (2) increasing efficiency and accuracy of simulations in time-varying evolution, and (3) debugging coalescence simulation software.

Further comments on "Vector norms as Lyapunov functions for linear systems"

This paper deals with the conditions for a vector norm to be a Lyapunov function for a linear time-invariant system. An error in the proof of the related theorem given in Hmamed (1994) is pointed out, and a counterexample proving that this theorem is generally false is provided. It is demonstrated that the considered problem is related to the one of extending a linear operator without increasing its norm.

Adaptive filtering of microarray gene expression data based on Gaussian mixture decomposition

BackgroundDNA microarrays are used for discovery of genes expressed differentially between various biological conditions. In microarray experiments the number of analyzed samples is often much lower than the number of genes (probe sets) which leads to many false discoveries. Multiple testing correction methods control the number of false discoveries but decrease the sensitivity of discovering differentially expressed genes. Concerning this problem, filtering methods for improving the power of detection of differentially expressed genes were proposed in earlier papers. These techniques are two-step procedures, where in the first step some pool of non-informative genes is removed and in the second step only the pool of the retained genes is used for searching for differentially expressed genes.ResultsA very important parameter to choose is the proportion between the sizes of the pools of removed and retained genes. A new method, which we propose, allow to determine close to optimal threshold values for sample means and sample variances for gene filtering. The method is adaptive and based on the decomposition of the histogram of gene expression means or variances into mixture of Gaussian components.ConclusionsBy performing analyses of several publicly available datasets and simulated datasets we demonstrate that our adaptive method increases sensitivity of finding differentially expressed genes compared to previous methods of filtering microarray data based on using fixed threshold values.

Comparison of peptide cancer signatures identified by mass spectrometry in serum of patients with head and neck, lung and colorectal cancers: Association with tumor progression

Mass spectrometry-based analyses of the low-molecular-weight fraction of serum proteome allow identifying proteome profiles (signatures) that are potentially useful in detection and diagnostics of cancer. Here we compared serum proteome profiles of healthy donors and patients with three different types of cancer aiming to identify peptide signatures that were either common for all cancer samples or specific for cancer type. Blood samples were collected before start of the therapy from patients with head and neck squamous cell cancer, colorectal adenocarcinoma and non-small cell lung cancer, and from a corresponding group of healthy volunteers. Mass profiles of the serum proteome were recorded in the range between 2 and 13 kDa using MALDI-ToF spectrometry and 131 identified peptide ions were used for statistical analyses. Similar degrees of overall similarities were observed in all intra-group and inter-group analyses when general features of serum proteome profiles were compared between individual samples. However, classifiers built of selected spectral components allowed differentiation between healthy donors and three groups of cancer patients with 69-74% sensitivity and 82-84% specificity. There were two common peptide species (3766 and 5867 Da) with increased levels in all cancer samples. Several spectral components permitted differentiation between lung cancer samples and either head and neck cancer or colorectal cancer samples, but two latter types of samples could not be properly discriminated. Abundance of spectral components that putatively corresponded to fragments of serum amyloid A (11511 and 11667 Da) was highest in lung cancer samples, yet increased levels of these peptides appeared to generally associate with more advanced cancer cases. We concluded that certain components of serum peptide signatures are common for different cancer signatures and putatively reflect general response of organism to the disease, yet other components of such signatures are more specific and most likely correspond to clinical stage of the malignancy.

BWtrs: A tool for searching for tandem repeats in DNA sequences based on the Burrows-Wheeler transform.

Genomes of organisms contain a variety of repeated structures of various length and type, interspersed or tandem. Tandem repeats play important role in molecular biology as they are related to genetic backgrounds of inherited diseases, and also they can serve as markers for DNA mapping and DNA fingerprinting. Improving the efficiency of algorithms for searching for tandem repeats in DNA sequences can lead to many useful applications in the area of genomics. We introduce a very efficient, web-based tool for large scale searching for exact tandem repeats in genomes, based on the use of the Burrows-Wheeler Transform. The service is a remarkably efficient and powerful application that allows analyzing complete genomes without any restrictions. The Burrows-Wheeler Tandem Repeat Searcher (BWtrs) is an on-line application that searches for the exact occurrences of tandem repetitions in DNA sequences. The BWtrs service is freely available at: http://bioinfo.polsl.pl/BWtrs. We present examples of the use of our web application and we compare results of our computations with the results obtained by using other existing tools for searches for exact tandem repeats.

First report on the patient database for the identification of the genetic pathways involved in patients over-reacting to radiotherapy: GENEPI-II

BACKGROUND Identifying the most radiosensitive patient group would have huge clinical implications. METHODS A tissue bank containing skin fibroblasts, whole blood, lymphocytes, plasma and lymphoblastoid cell lines from clinically radiation hypersensitive patients was established from patients in Europe and Canada. Over-reacting individuals had CTCAE3.0 severe acute side effects grade 2 or more occurring at very low radiation doses where these side effects are unexpected or grade 3-4 lasting more than 4 weeks after the end of radiotherapy and/or requiring surgical intervention at any time or severe late side effects grade 3-4. RESULTS Eleven patients have been identified with a mean age of 61.6±8.5 years (range 49-74). Two patients were male, 9 female. One patient had non-small cell lung cancer, 6 breast cancer, 2 head and neck cancer, one lymphoma and one meningioma. The mean follow-up time after radiotherapy was 1658±1048 days (range 84-3752). CONCLUSIONS The establishment of an international tissue bank of the rare group of patients with extreme hypersensitivity to radiotherapy was proven to be feasible and should enable in-depth molecular studies.