Mutation model for nucleotide sequences based on crystal basis

A nucleotides sequence is identified, in the two (four) letters alphabet, by the the labels of a vector state of an irreducible representation of U_q(sl(2)) (U_q(sl(2) + sl(2))), in the limit q -> 0. A master equation for the distribution function is written, where the intensity of the one-spin flip is assumed to depend from the variation of the labels of the state. In the two letters approximation, the numerically computed equilibrium distribution for short sequences is nicely fitted by a Yule distribution, which is the observed distribution of the ranked short oligonucleotides frequency in DNA. The four letter alphabet description, applied to the codons, is able to reproduce the form of the fitted rank ordered usage frequencies distribution.Comment: 27 pages, 9 figure

Prospective teachers' interpretative knowledge: giving sense to subtraction algorithms

The process of interpretation and assessment of students’ mathematical productions represents a crucial aspect of teachers’ practices. In such processes, teachers rely on the so-called interpretative knowledge, which includes particular aspects of their mathematical and pedagogical knowledge, their view of mathematics, and their values. In this paper, we analyze and discuss prospective primary teachers’ interpretative knowledge gained through their assessment of different subtraction algorithms

The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007

In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position--specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented. We demonstrate that the mean--field approximation, which is also known as context--free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.Comment: Significantly extended version with new data for all the 348 distinct bacterial genomes available in Genbank in April 200

Universality and Shannon entropy of codon usage

The distribution functions of the codon usage probabilities, computed over all the available GenBank data, for 40 eukaryotic biological species and 5 chloroplasts, do not follow a Zipf law, but are best fitted by the sum of a constant, an exponential and a linear function in the rank of usage. For mitochondriae the analysis is not conclusive. A quantum-mechanics-inspired model is proposed to describe the observed behaviour. These functions are characterized by parameters that strongly depend on the total GC content of the coding regions of biological species. It is predicted that the codon usage is the same in all exonic genes with the same GC content. The Shannon entropy for codons, also strongly depending on the exonic GC content, is computed.Comment: Latex 25 pages, 21 figure

HBeAg Levels Vary across the Different Stages of HBV Infection According to the Extent of Immunological Pressure and Are Associated with Therapeutic Outcome in the Setting of Immunosuppression-Driven HBV Reactivation

HBeAg is a marker of HBV-activity, and HBeAg-loss predicts a favorable clinical outcome. Here, we characterize HBeAg-levels across different phases of HBV infection, their correlation with virological/biochemical markers and the virological response to anti-HBV therapy. Quantitative HBeAg (qHBeAg, DiaSorin) is assessed in 101 HBeAg+ patients: 20 with acute-infection, 20 with chronic infection, 32 with chronic hepatitis and 29 with immunosuppression-driven HBV-reactivation (HBV-R). A total of 15/29 patients with HBV-R are monitored for > 12 months after starting TDF/ETV. qHBeAg is higher in immunosuppression-driven HBV-R (median[IQR]:930[206-1945]PEIU/mL) and declines in chronic hepatitis (481[28-1393]PEIU/mL, p = 0.03), suggesting HBeAg production, modulated by the extent of immunological pressure. This is reinforced by the negative correlation between qHBeAg and ALT in acute infection (Rho = -0.66, p = 0.006) and chronic hepatitis (Rho = -0.35; p = 0.05). Interestingly, qHBeAg strongly and positively correlates with qHBsAg across the study groups, suggesting cccDNA as a major source of both proteins in the setting of HBeAg positivity (with limited contribution of integrated HBV-DNA to HBsAg production). Focusing on 15 patients with HBV-R starting TDF/ETV, virological suppression and HBeAg-loss are achieved in 60% and 53.3%. Notably, the combination of qHBeAg > 2000 PEIU/mL + qHBsAg > 52,000 IU/mL at HBV-R is the only factor predicting no HBeAg loss (HBeAg loss: 0% with vs. 72.7% without qHBeAg > 2000 PEIU/mL + qHBsAg > 52,000 IU/mL, p = 0.03). In conclusion, qHBeAg varies over the natural course of HBV infection, according to the extent of immunological pressure. In the setting of HBV-R, qHBeAg could be useful in predicting the treatment response under immunosuppression

Decline of Prevalence of Resistance Associated Substitutions to NS3 and NS5A inhibitors at DAA-failure in Hepatitis C Virus in Italy over the years 2015 to 2018

Background: A minority of patients fail to eliminate HCV and resistance-associated substitutions (RASs) are commonly detected at failure of interferon-free DAA regimens. Material and methods: Within the Italian network VIRONET-C, the prevalence of NS3/NS5A/NS5B RASs was retrospectively evaluated in patients who failed an EASL recommended DAA-regimen in 2015-2018. NS3, NS5A and NS5B Sanger sequencing was performed using homemade protocols. The geno2pheno system was used to infer HCV-genotype/subtype and predict drug resistance. The changes in the prevalence of RASs over time were evaluated using the chi-square test for trend, predictors of RASs at failure were analysed by logistic regression. Results: We included 386 real-life HCV pts failed to recommended DAA regimens: 92% (271/294) Italians, 75% (286/384) males, median age was 56 years (IQR 52-61); 106 (28%) were treatment-experienced: 91 (86%) with IFN-based treatments, 26 (25%) with DAA-based regimens. Metavir fibrosis stage was F4 in 76% (245/322), 65% (240/369) had clinical cirrhosis. Patients with HIV and HBV coinfection were 10% (33/317) and 8% (6/72), respectively. HCV genotype (G) was G1b in 122 pts (32%), G3a 103 (27%), G1a 97 (25%), G4d 30 (8%), G2c 19 (5%), G3h 5 (1.3%), G4a 4 (1%) and 1 (0.3%) each for G3g, G4n/o/v. DAA regimens were: LDV/SOF in 115 (30%), DCV/SOF in 103 (27%), 3D in 83 (21%), EBR/GRZ in 32 (8%), VEL/SOF in 29 (7%), GLE/PIB in 18 (5%) and 2D in 6 (2%); ribavirin was administered in 123 (32%). Antiviral treatment was completed by 352 pts (91%), while 34 (9%) discontinued prematurely. The NS5A fasta-sequence was available for all pts, NS5B for 361 (94%), NS3 for 365 (95%). The prevalence of any RASs was 87%, namely 78/135 (58%) in NS3, 303/359 (85%) in NS5A, 114/286 (40%) in NS5B (Tab 1). The prevalence of any RASs significantly declined from 2015 to 2018 (100%, 13/13 vs 81%, 101/125, p=0.01): NS5A RASs from 100%, 13/13 to 76%, 76/100 (p<0.001), NS3 RASs from 88%, 7/8 to 44%, 28/63 (p=0.02), while NS5B RASs remained stable. Independent predictors of any RASs included liver cirrhosis/advanced fibrosis (AOR 3.72, CI 95% 1.51-9.17, p=0.004) and genotype (G2 vs G1a AOR 0.01, CI 95% 0.0-0.3, p<0.001; G3 vs G1a AOR 0.22, CI 95% 0.05-0.98, p<0.047; G4 vs G1a AOR 0.13, CI 95% 0.03-0.63, p<0.011), with a modest effect scored for past treatment (AOR 3.45, CI 95% 1.00-11.92, p=0.05), after adjusting for DAA regimen and year of genotype. Notably, full activity was predicted for GLE/PIB in 75.9% of cases and for at least two components of VEL/SOF/VOX in 59% of cases and no case with full-resistance to either regimen was found (Tab 2). Conclusions: Despite decreasing prevalence over the years, RASs remain a common signature at virological failure of DAA treatment, particularly in patients with the highest grade of liver fibrosis. Their distribution may vary according to genotype, so the identification of RASs after failure could play a crucial role in optimizing retreatment strategies

DECLINE OF PREVALENCE OF RESISTANCE ASSOCIATED SUBSTITUTIONS TO NS3 AND NS5A INHIBITORS AT DAA- FAILURE IN HEPATITIS C VIRUS IN ITALY OVER THE YEARS 2015 TO 2018

Background: A minority of patients fails to eliminate HCV and resistance-associated substitutions (RASs) are commonly detected at failure of interferon-free DAA regimens . Methods: Within the Italian network VIRONET-C, the prevalence of NS3/NS5A/NS5B RASs was retrospectively evaluated in patients who failed an EASL recommended DAA-regimen in 2015-2018 . The geno2pheno system and Sorbo MC et al. Drug Resistance Updates 2018 were used to infer HCV- genotype/subtype and predict drug resistance . The changes in prevalence of RASs over time were evaluated by chi-square test for trend, predictors of RASs at failure were analysed by logistic regression . Results: We included 386 HCV infected patients: 75% males, median age was 56 years (IQR 52-61), metavir fibrosis stage F4 in 76%; 106 (28%) were treatment- experienced: 91 (86%) with IFN-based treatments, 26 (25%) with DAAs. Patients with HIV and HBV coinfection were 10% (33/317) and 8% (6/72), respectively. HCV genotype was 1b in 122 pts (32%), 3 in 109 (28%), 1a in 97 (25%), 4 in 37 (10%), 2 in 21 (5%). DAA regimens were: LDV/SOF in 115 (30%), DCV/SOF in 103 (27%), 3D in 83 (21%), EBR/GRZ in 32 (8%), VEL/SOF in 29 (7%), GLE/PIB in 18 (5%) and 2D in 6 (2%); ribavirin was administered in 123 (32%) . The NS5A fasta-sequence was available for all patients, NS5B for 361 (94%), NS3 for 365 (95%) . According to the DAA failed the prevalence of any RASs was 90%, namely 80/135 (59%) in NS3, 313/359 (87%) in NS5A, 114/286 (40%) in NS5B . The prevalence of any RASs significantly declined from 2015 to 2018 (93% vs 70%, p=0.004): NS5A RASs from 90% to 72% (p=0 .29), NS3 RASs from 74% to 18% (p<0 .001), while NS5B RASs remained stable . Independent predictors of any RASs included advanced fibrosis (AOR 6.1, CI 95% 1.8-20.3, p=0 .004) and genotype (G2 vs G1a AOR 0 .03, CI 95% 0 .002- 0 .31, p=0 .004; G3 vs G1a AOR 0 .08, CI 95% 0 .01-0 .62, p=0 .02; G4 vs G1a AOR 0 .05, CI 95% 0 .006-0 .46, p=0 .008), after adjusting for age, previous HCV treatment and year of genotype . Notably, full activity was predicted for GLE/PIB in 75% of cases and for at least two components of VEL/SOF/VOX in 53% of cases, no case with full-resistance to either regimen was found . Conclusion: Despite decreasing prevalence over the years, RASs remain common at virological failure of DAA treatment, particularly in patients with the highest grade of liver fibrosis. The identification of RASs after failure could play a crucial role in optimizing retreatment strategies