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In the package corr2D two-dimensional correlation analysis is implemented in R. This paper describes how two-dimensional correlation analysis is done in the package and how the mathematical equations are translated into R code. The paper features a simple tutorial with executable code for beginners, insight into the calculations done before the correlation analysis, a detailed look at the parallelization of the fast Fourier transformation based correlation analysis and a speed test of the calculation. The package corr2D offers the possibility to preprocess, correlate and postprocess spectroscopic data using exclusively the R language. Thus, corr2D is a welcome addition to the toolbox of spectroscopists and makes two-dimensional correlation analysis more accessible and transparent.

Dermal fibroblast cells can adopt different cell states such as proliferation, quiescence, apoptosis or senescence, in order to ensure tissue homeostasis. Proliferating (dividing) cells pass through the phases of the cell cycle, while quiescent and senescent cells exist in a non-proliferating cell cycle-arrested state. However, the reversible quiescence state is in contrast to the irreversible senescence state. Long-term quiescent cells transit into senescence indicating that cells age also when not passing through the cell cycle. Here, by label-free in vitro vibrational spectroscopy, we studied the biomolecular composition of quiescent dermal fibroblast cells and compared them with those of proliferating and senescent cells. Spectra were examined by multivariate statistical analysis using a PLS-LDA classification model, revealing differences in the biomolecular composition between the cell states mainly associated with protein alterations (variations in the side chain residues of amino acids and protein secondary structure), but also within nucleic acids and lipids. We observed spectral changes in quiescent compared to proliferating cells, which increased with quiescence cultivation time. Raman and infrared spectroscopy, which yield complementary biochemical information, clearly distinguished contact-inhibited from serum-starved quiescent cells. Furthermore, the spectra displayed spectral differences between quiescent cells and proliferating cells, which had recovered from quiescence. This became more distinct with increasing quiescence cultivation time. When comparing proliferating, (in particular long-term) quiescent and senescent cells, we found that Raman as well as infrared spectroscopy can separate these three cellular states from each other due to differences in their biomolecular composition. Our spectroscopic analysis shows that proliferating and quiescent fibroblast cells age by similar but biochemically not identical processes. Despite their aging induced changes, over long time periods quiescent cells can return into the cell cycle. Finally however, the cell cycle arrest becomes irreversible indicating senescence.Dermal fibroblast cells can adopt different cell states such as proliferation, quiescence, apoptosis or senescence, in order to ensure tissue homeostasis. Proliferating (dividing) cells pass through the phases of the cell cycle, while quiescent and senescent cells exist in a non-proliferating cell cycle-arrested state. However, the reversible quiescence state is in contrast to the irreversible senescence state. Long-term quiescent cells transit into senescence indicating that cells age also when not passing through the cell cycle. Here, by label-free in vitro vibrational spectroscopy, we studied the biomolecular composition of quiescent dermal fibroblast cells and compared them with those of proliferating and senescent cells. Spectra were examined by multivariate statistical analysis using a PLS-LDA classification model, revealing differences in the biomolecular composition between the cell states mainly associated with protein alterations (variations in the side chain residues of amino acids and protein secondary structure), but also within nucleic acids and lipids. We observed spectral changes in quiescent compared to proliferating cells, which increased with quiescence cultivation time. Raman and infrared spectroscopy, which yield complementary biochemical information, clearly distinguished contact-inhibited from serum-starved quiescent cells. Furthermore, the spectra displayed spectral differences between quiescent cells and proliferating cells, which had recovered from quiescence. This became more distinct with increasing quiescence cultivation time. When comparing proliferating, (in particular long-term) quiescent and senescent cells, we found that Raman as well as infrared spectroscopy can separate these three cellular states from each other due to differences in their biomolecular composition. Our spectroscopic analysis shows that proliferating and quiescent fibroblast cells age by similar but biochemically not identical processes. Despite their aging induced changes, over long time periods quiescent cells can return into the cell cycle. Finally however, the cell cycle arrest becomes irreversible indicating senescence.

Recently a new family of loss functions called smart error sums has been suggested. These loss functions account for correlations within experimental data and force modeled data to obey these correlations. As a result, multiplicative systematic errors of experimental data can be revealed and corrected. The smart error sums are based on 2D correlation analysis which is a comparably recent methodology for analyzing spectroscopic data that has found broad application. In this contribution we mathematically generalize and break down this methodology and the smart error sums to uncover the mathematic roots and simplify it to craft a general tool beyond spectroscopic modelling. This reduction also allows a simplified discussion about limits and prospects of this new method including one of its potential future uses as a sophisticated loss function in deep learning. To support its deployment, the work includes computer code to allow reproduction of the basic results.

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