RESUMO
We use persistent homology and persistence images as an observable of three variants of the two-dimensional XY model to identify and study their phase transitions. We examine models with the classical XY action, a topological lattice action, and an action with an additional nematic term. In particular, we introduce a way of computing the persistent homology of lattice spin model configurations and, by considering the fluctuations in the output of logistic regression and k-nearest neighbor models trained on persistence images, we develop a methodology to extract estimates of the critical temperature and the critical exponent of the correlation length. We put particular emphasis on finite-size scaling behavior and producing estimates with quantifiable error. For each model we successfully identify its phase transition(s) and are able to get an accurate determination of the critical temperatures and critical exponents of the correlation length.
RESUMO
The development of hypoxia-selective radiopharmaceuticals for use as therapeutic and/or imaging agents is of vital importance for both early identification and treatment of cancer and in the design of new drugs. Radiotracers based on copper for use in positron emission tomography have received great attention due to the successful application of copper(II) bis(thiosemicarbazonato) complexes, such as [(60/62/64)Cu(II)ATSM] and [(60/62/64)Cu(II)PTSM], as markers for tumour hypoxia and blood perfusion, respectively. Recent work has led to the proposal of a revised mechanism of hypoxia-selective cellular uptake and retention of [Cu(II)ATSM]. The work presented here describes non-steady-state kinetic simulations in which the reported pO(2)-dependent in vitro cellular uptake and retention of [(64)Cu(II)ATSM] in EMT6 murine carcinoma cells has been modelled by using the revised mechanistic scheme. Non-steady-state (NSS) kinetic analysis reveals that the model is in very good agreement with the reported experimental data with a root-mean-squared error of less than 6% between the simulated and experimental cellular uptake profiles. Estimated rate constants are derived for the cellular uptake and washout (k(1) = 9.8 +/- 0.59 x 10(-4) s(-1) and k(2) = 2.9 +/- 0.17 x 10(-3) s(-1)), intracellular reduction (k(3) = 5.2 +/- 0.31 x 10(-2) s(-1)), reoxidation (k(4) = 2.2 +/- 0.13 mol(-1) dm(3) s(-1)) and proton-mediated ligand dissociation (k(5) = 9.0 +/- 0.54 x 10(-5) s(-1)). Previous mechanisms focused on the reduction and reoxidation steps. However, the data suggest that the origins of hypoxia-selective retention may reside with the stability of the copper(I) anion with respect to protonation and ligand dissociation. In vitro kinetic studies using the nicotimamide adenine dinucleotide (NADH)-dependent ferredoxin reductase enzyme PuR isolated from the bacterium Rhodopseudomonas palustris have also been conducted. NADH turnover frequencies are found to be dependent on the structure of the ligand and the results confirm that the proposed reduction step in the mechanism of hypoxia selectivity is likely to be mediated by NADH-dependent enzymes. Further understanding of the mechanism of hypoxia selectivity may facilitate the development of new imaging and radiotherapeutic agents with increased specificity for tumour hypoxia.
