Matematyka z komputerem. Ćwiczenia dla studentów realizowane za pomocą pakietu Maxima.

Wydanie III poprawione, uzupełnione i rozszerzone – wersja elektroniczna Opublikowano w grudniu 2017 rProponowany Czytelnikowi skrypt przedstawia możliwości, jakie daje praca z Systemem Algebry Komputerowej (CAS) Maxima, wspomagającym wykonywanie matematycznych obliczeń symbolicznych oraz numerycznych. Pozycja ta kierowana jest do studentów, którzy, uczestnicząc w ćwiczeniach laboratoryjnych w pracowni komputerowej, mają możliwość uzupełniania zdobywanej wiedzy matematycznej o doświadczenia związane ze stosowaniem technologii informatycznych oraz do wszystkich, chcących skorzystać z programu Maxima jako narzędzia do rozwiązywania problemów matematycznych i technicznych. Program Maxima jest pomocnym narzędziem do wizualizacji różnych zagadnień. Umożliwia lepsze i szybsze zrozumienie teorii matematycznych, pozwala kontrolować kolejne etapy obliczeń, rozważać różne sposoby rozwiązywania problemów i interpretować uzyskane wyniki, a także wyeliminować błędy w przypadku skomplikowanych rachunków. Operacje mogą być wykonywane nie tylko na liczbach, także na zmiennych oraz funkcjach. Jak każde narzędzie informatyczne, nie jest to program pozbawiony wad, więc należy krytycznie podchodzić do uzyskanych wyników i mieć świadomość ograniczeń programu, z którymi możemy się zetknąć podczas zajęć laboratoryjnych. Maxima jest programem bezpłatnym i otwartym, stale rozwijanym przez społeczność użytkowników W skrypcie zostały przedstawione rozwiązania zadań przykładowych z wykorzystaniem Maximy w wersji 5.31.2 oraz zadania do samodzielnego rozwiązania wraz z odpowiedziami. Wśród zadań przykładowych, jak i zadań do samodzielnego rozwiązania, można znaleźć takie, które ilustrują zastosowanie teorii matematycznych w analizie zagadnień optymalizacyjnych, fizycznych i ekonomicznych. Do obecnego wydania skryptu dołączono następujące nowe rozdziały: Rozdział 13. Szeregi Fouriera, Rozdział 16. Funkcja uwikłana jednej zmiennej, Rozdział 20. Pakiet Simplex. W skrypcie zostały przedstawione rozwiązania zadań przykładowych do nowych rozdziałów, bogato ilustrowane graficznie, z wykorzystaniem Maximy w wersji 5.40.0 oraz kolejne zadania do samodzielnego rozwiązania wraz z odpowiedziami

The prevalence of autoimmune diseases in patients with type 1 diabetes and in their relatives

Wstęp. Cukrzyca typu 1 to choroba o podłożu autoimmunologicznym, która może występować samodzielnie bądź może być skojarzona z innymi chorobami autoimmunizacyjnymi. Celem badania była ocena częstości występowania chorób autoimmunologicznych u pacjentów z cukrzycą typu 1 oraz u ich krewnych.Materiał i metody. W badaniu wzięło udział 219 pacjentów (85 kobiet i 134 mężczyzn) chorych na cukrzycę typu 1 i będących pod stałą opieką Poradni Diabetologicznej. Przeprowadzono badanie ankietowe dotyczące występowania chorób autoimmunologicznychu pacjenta i jego krewnych oraz poddano starannejanalizie dokumentację medyczną poradni. Projektbadania zaakceptowała Komisja Bioetyki UniwersytetuMedycznego w Łodzi.Wyniki. W przeprowadzonych badaniach najczęstsząchorobą autoimmunologiczną rozpoznawaną u pacjentówz cukrzycą typu 1 była choroba Hashimoto(odnotowano ją u 17,35% badanych). Kolejne co doczęstości występowania choroby autoimmunologiczneodnotowane w badanej populacji to bielactwo, celiakia,reumatoidalne zapalenie stawów i łysienie plackowate.W przypadku 32 pacjentów (14,61%) obserwowano występowanie cukrzycy typu 1 u krewnych, poza cukrzycązaś najczęściej występującą wśród nich chorobą autoimmunologiczną było reumatoidalne zapalenie stawów.Wnioski. Cukrzyca typu 1 stanowi niewątpliwy czynnikryzyka wystąpienia dodatkowej choroby o podłożuautoimmunologicznym — najczęstszą chorobą stwierdzaną w badanej populacji była choroba Hashimoto, dlatego u wszystkich pacjentów chorych na cukrzycę typu 1 powinno się wykonywać badania przesiewowe w kierunku autoimmunologicznego zapalenia tarczycy.Introduction. Type 1 diabetes is an autoimmunedisease, which can affect a patient either alone or inconjunction with other diseases of the autoimmunebackground. The aim of the study is assessment of theincidence of the other autoimmune diseases in type 1diabetes patients and in their relatives.Material and methods. The study was performed in219 type 1 diabetic subjects (85 female and 134 male).A comorbidity of the other autoimmune diseases insubjects and their relatives were studied using a specific questionnaire and patient’s medical records. Theproject of the study was approved by the Commissionof Bioethics, Medical University of Lodz.Results. Hashimoto’s thyroiditis was the most frequentautoimmune comorbidityin the examined subjects(17.35%). The less frequent autoimmune diseasescoexisting with type 1 diabetes were: vitilogo, celiacdisease, rheumatoid arthritis and alopecia areata. In32 subjects (14.61%) family history of type 1 diabeteswas also reported. Besides diabetes among fi rst degreerelatives rheumatoid arthritis was the most frequentautoimmune disease.Conclusions. Type 1 diabetes is a risk factor for theother autoimmune diseases and Hashimoto’s thyroiditisis the most common comorbidity, thus screeningfor autoimmune thyroiditis should be performed inpatients with type 1 diabetes

Molecular characterization of the PhiKo endolysin from Thermus thermophilus HB27 bacteriophage phiKo and its cryptic lytic peptide RAP-29

IntroductionIn the era of increasing bacterial resistance to antibiotics, new bactericidal substances are sought, and lysins derived from extremophilic organisms have the undoubted advantage of being stable under harsh environmental conditions. The PhiKo endolysin is derived from the phiKo bacteriophage infecting Gram-negative extremophilic bacterium Thermus thermophilus HB27. This enzyme shows similarity to two previously investigated thermostable type-2 amidases, the Ts2631 and Ph2119 from Thermus scotoductus bacteriophages, that revealed high lytic activity not only against thermophiles but also against Gram-negative mesophilic bacteria. Therefore, antibacterial potential of the PhiKo endolysin was investigated in the study presented here.MethodsEnzyme activity was assessed using turbidity reduction assays (TRAs) and antibacterial tests. Differential scanning calorimetry was applied to evaluate protein stability. The Collection of Anti-Microbial Peptides (CAMP) and Antimicrobial Peptide Calculator and Predictor (APD3) were used to predict regions with antimicrobial potential in the PhiKo primary sequence. The minimum inhibitory concentration (MIC) of the RAP-29 synthetic peptide was determined against Gram-positive and Gram-negative selected strains, and mechanism of action was investigated with use of membrane potential sensitive fluorescent dye 3,3′-Dipropylthiacarbocyanine iodide (DiSC3(5)).Results and discussionThe PhiKo endolysin is highly thermostable with melting temperature of 91.70°C. However, despite its lytic effect against such extremophiles as: T. thermophilus, Thermus flavus, Thermus parvatiensis, Thermus scotoductus, and Deinococcus radiodurans, PhiKo showed moderate antibacterial activity against mesophiles. Consequently, its protein sequence was searched for regions with potential antibacterial activity. A highly positively charged region was identified and synthetized (PhiKo105-133). The novel RAP-29 peptide lysed mesophilic strains of staphylococci and Gram-negative bacteria, reducing the number of cells by 3.7–7.1 log units and reaching the minimum inhibitory concentration values in the range of 2–31 μM. This peptide is unstructured in an aqueous solution but forms an α-helix in the presence of detergents. Moreover, it binds lipoteichoic acid and lipopolysaccharide, and causes depolarization of bacterial membranes. The RAP-29 peptide is a promising candidate for combating bacterial pathogens. The existence of this cryptic peptide testifies to a much wider panel of antimicrobial peptides than thought previously

Evaluation of GFP reporter utility for analysis of transcriptional slippage during gene expression

Abstract Background Epimutations arising from transcriptional slippage seem to have more important role in regulating gene expression than earlier though. Since the level and the fidelity of transcription primarily determine the overall efficiency of gene expression, all factors contributing to their decrease should be identified and optimized. Results To examine the influence of A/T homopolymeric sequences on introduction of erroneous nucleotides by slippage mechanism green fluorescence protein (GFP) reporter was chosen. The in- or out-of-frame gfp gene was fused to upstream fragment with variable number of adenine or thymine stretches resulting in several hybrid GFP proteins with diverse amino acids at N-terminus. Here, by using T7 phage expression system we showed that the intensity of GFP fluorescence mainly depends on the number of the retained natural amino acids. While the lack of serine (S2) residue results in negligible effects, the lack of serine and lysine (S2K3) contributed to a significant reduction in fluorescence by 2.7-fold for polyA-based in-frame controls and twofold for polyTs. What is more, N-terminal tails amino acid composition was rather of secondary importance, since the whole-cell fluorescence differed in a range of 9–18% between corresponding polyA- and polyT-based constructs. Conclusions Here we present experimental evidence for utility of GFP reporter for accurate estimation of A/T homopolymeric sequence contribution in transcriptional slippage induction. We showed that the intensity of GFP hybrid fluorescence mainly depends on the number of retained natural amino acids, thus fluorescence raw data need to be referred to appropriate positive control. Moreover, only in case of GFP hybrids with relatively short N-terminal tags the fluorescence level solely reflects production yield, what further indicates the impact of an individual slippage sequence. Our results demonstrate that in contrast to the E. coli enzyme, T7 RNA polymerase exhibits extremely high propensity to slippage even on runs as short as 3 adenine or 4 thymine residues

Influence of Pine and Alder Woodchips Storage Method on the Chemical Composition and Sugar Yield in Liquid Biofuel Production

The aim of this study was to investigate the effect of storing methods of woodchips from two species, pine (Pinus sylvestris L.) and alder (Alnus Mill.), on the basic chemical composition and sugar yield in liquid biofuel production. Two methods of storing woody biomass were used in the study—an open pile and a cover pile. The wood was felled at the end of November and was stored as industrial chips for eight months from December onward. After this time, material was collected for chemical composition analyses and enzymatic hydrolysis. The results of the chemical composition analysis of the wood for both studied species showed the influence of the type of storage on the composition of the individual structural components of the wood. Based on the results of the enzymatic hydrolysis of the woody biomass, it can be seen that, irrespective of the hydrolysed material (wood, cellulose, holocellulose), the material from the biomass stored in the open pile gave higher results. The hydrolysis efficiency also increased with time, independent of the type of material that was hydrolysed. The highest sugar yield from the enzymatic hydrolysis of wood was obtained for alder wood stored in an open pile. The highest sugar yield from the enzymatic hydrolysis of cellulose was obtained for cellulose extracted from alder wood—as well—that had been stored in an open pile

Molecular Characterization of a Novel Lytic Enzyme LysC from Clostridium intestinale URNW and Its Antibacterial Activity Mediated by Positively Charged N-Terminal Extension

Peptidoglycan hydrolytic enzymes are considered to be a promising alternative to conventional antibiotics in combating bacterial infections. To identify novel hydrolytic enzymes, we performed a database search with the sequences of two thermostable endolysins with high bactericidal activity, studied earlier in our laboratory. Both these enzymes originate from Thermus scotoductus bacteriophages MAT2119 and vB_Tsc2631. A lytic enzyme LysC from Clostridium intestinale URNW was found to have the highest amino acid sequence similarity to the bacteriophage proteins and was chosen for further analysis. The recombinant enzyme showed strong activity against its host bacteria C. intestinale, as well as against C. sporogenes, Bacillus cereus, Micrococcus luteus, and Staphylococcus aureus, on average causing a 5.12 ± 0.14 log reduction of viable S. aureus ATCC 25923 cells in a bactericidal assay. Crystallographic studies of the protein showed that the catalytic site of LysC contained a zinc atom coordinated by amino acid residues His50, His147, and Cys155, a feature characteristic for type 2 amidases. Surprisingly, neither of these residues, nor any other of the four conserved residues in the vicinity of the active site, His51, Thr52, Tyr76, and Thr153, were essential to maintain the antibacterial activity of LysC. Therefore, our attention was attracted to the intrinsically disordered and highly positively charged N-terminal region of the enzyme. Potential antibacterial activity of this part of the sequence, predicted by the Antimicrobial Sequence Scanning System, AMPA, was confirmed in our experimental studies; the truncated version of LysC (LysCΔ2–23) completely lacked antibacterial activity. Moreover, a synthetic peptide, which we termed Intestinalin, with a sequence identical to the first thirty amino acids of LysC, displayed substantial anti-staphylococcal activity with IC50 of 6 μg/mL (1.5 μM). This peptide was shown to have α-helical conformation in solution in the presence of detergents which is a common feature of amphipathic α-helical antimicrobial peptides

Data_Sheet_1_Molecular characterization of the PhiKo endolysin from Thermus thermophilus HB27 bacteriophage phiKo and its cryptic lytic peptide RAP-29.docx

IntroductionIn the era of increasing bacterial resistance to antibiotics, new bactericidal substances are sought, and lysins derived from extremophilic organisms have the undoubted advantage of being stable under harsh environmental conditions. The PhiKo endolysin is derived from the phiKo bacteriophage infecting Gram-negative extremophilic bacterium Thermus thermophilus HB27. This enzyme shows similarity to two previously investigated thermostable type-2 amidases, the Ts2631 and Ph2119 from Thermus scotoductus bacteriophages, that revealed high lytic activity not only against thermophiles but also against Gram-negative mesophilic bacteria. Therefore, antibacterial potential of the PhiKo endolysin was investigated in the study presented here.MethodsEnzyme activity was assessed using turbidity reduction assays (TRAs) and antibacterial tests. Differential scanning calorimetry was applied to evaluate protein stability. The Collection of Anti-Microbial Peptides (CAMP) and Antimicrobial Peptide Calculator and Predictor (APD3) were used to predict regions with antimicrobial potential in the PhiKo primary sequence. The minimum inhibitory concentration (MIC) of the RAP-29 synthetic peptide was determined against Gram-positive and Gram-negative selected strains, and mechanism of action was investigated with use of membrane potential sensitive fluorescent dye 3,3′-Dipropylthiacarbocyanine iodide (DiSC3(5)).Results and discussionThe PhiKo endolysin is highly thermostable with melting temperature of 91.70°C. However, despite its lytic effect against such extremophiles as: T. thermophilus, Thermus flavus, Thermus parvatiensis, Thermus scotoductus, and Deinococcus radiodurans, PhiKo showed moderate antibacterial activity against mesophiles. Consequently, its protein sequence was searched for regions with potential antibacterial activity. A highly positively charged region was identified and synthetized (PhiKo105-133). The novel RAP-29 peptide lysed mesophilic strains of staphylococci and Gram-negative bacteria, reducing the number of cells by 3.7–7.1 log units and reaching the minimum inhibitory concentration values in the range of 2–31 μM. This peptide is unstructured in an aqueous solution but forms an α-helix in the presence of detergents. Moreover, it binds lipoteichoic acid and lipopolysaccharide, and causes depolarization of bacterial membranes. The RAP-29 peptide is a promising candidate for combating bacterial pathogens. The existence of this cryptic peptide testifies to a much wider panel of antimicrobial peptides than thought previously.</p