# Application of Advanced Non-Linear Spectral Decomposition and Regression Methods for Spectroscopic Analysis of Targeted and Non-Targeted Irradiation Effects in an In-Vitro Model

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

^{−1}), rather than alterations across the spectrum as seen in other works. This alteration is due to a biochemical species which remains unidentified.

## 2. Results

#### 2.1. Visualisation of Spectra

#### 2.2. PCA-SVM Modelling

_{1}-score used as the metric of classification performance, and models were generated for 20 separate data randomisation epochs.

_{1}scores at cross-validation in excess of 0.97 at both training and testing. Figure 5 depicts the loadings to principal components 1 to 3.

#### 2.3. CLS Spectral Fitting

#### 2.4. XGBoost Regression against Cell Volume

## 3. Discussion

^{−1}and ν C-O of RNA in the region of 1112 cm

^{−1}; ν as -C=O DNA, RNA in the region of 1696 and 1716), carbohydrate (νC-O in the region of 1202 cm

^{−1}; O-H deformation in the region of 1220 cm

^{−1}; ν O-H in the region from 3300 to 3488 cm

^{−1}), and protein (Amide II in the region of 1532 cm

^{−1}; Amide I 1654 cm

^{−1}) predominate, with some loadings to vibrations of methyl terminals (−CH

_{2}and −CH

_{3}νs and νas from 2840 to 2968 cm

^{−1}).

^{−1}) and Amide I vibrations (1626 cm

^{−1}and 1658 cm

^{−1}) appear to have shifted downwards by between 4 cm

^{−1}and 6 cm

^{−1}. Likewise the positions of the vibrations of methyl terminals in LV1 (2840 cm

^{−1}to 2968 cm

^{−1}), LV2 (2956 cm

^{−1}) and LV3 (2846 cm

^{−1}to 2968 cm

^{−1}) are shifted by between 4 cm

^{−1}and 10 cm

^{−1}, again towards lower vibrational frequencies. Each of these features suggests a weakening of structural strength within protein and lipid associated with cell signalling and cell death mechanisms owing to low dose irradiation.

_{2}(in the region of 2856 cm

^{−1}) and νs, νas vibrations of −CH

_{3}(at 2932 cm

^{−1}and 2964 cm

^{−1}). In the latter instance these vibrational modes appear to be shifted towards higher vibrational frequencies by between 4 cm

^{−1}and 12 cm

^{−1}, which is generally associated with the strengthening of the vibration. This suggests a spectral signature which potentially differentiates cells on exposure mode, with a weakening of the vibrational strength of protein and lipid seen in response to indirect (bystander) irradiation with a strengthening of the vibrations of methyl moieties in protein and lipid in response to direct irradiation. While this is an interesting feature which has not previously been observed it is difficult, in the absence of parallel biochemical assays, to ascribe any potential biological origin for this signal, and this remains an opportunity for further investigation.

- A reduction in colony volume between the PNT1A cells exposed to 0.2 Gy (PNT1A OF) and in unirradiated cells exposed to secreted factors from the tumour cells (PNT1A 0 Gy ICCM) when compared to cells irradiated with a low dose prior to exposure to secreted factors from the tumour (PNT1A OF ICCM);
- An increase in DNA double strand break (DSB) damage foci (γH2AX fluorescence measured via confocal microscopy) for all exposure modes, with the exposure of PNT1A cells to both a dose of 0.2 Gy and secreted factors from the tumour cells (PNT1A OF ICCM) producing a statistically significant increase in damage relative to the other exposure modes.

^{−1}to 1152 cm

^{−1}which are generally associated with the ν C-O vibrations in carbohydrate. The remainder of the features which are most commonly selected by the models across each independent epoch are those in the region from 998 to 1016 cm

^{−1}which are again associated with stretching of the C-O moiety in carbohydrate, and those from 3320 to 3568 cm

^{−1}which are associated with the stretching vibration in the O-H groups of carbohydrate. Taken in their totality this suggests that the spectral features associated with carbohydrate moieties such as C-O and O-H may be considered as a spectral marker of cell proliferation as measured by cell volume.

## 4. Materials and Methods

#### 4.1. Sample Preparation and Characteristics

#### 4.1.1. Cell Culture, Irradiation, Exposure to Irradiated Cell Culture Medium (ICCM) and Parallel Biological Assays

^{®}, Wicklow, Ireland) which contained 10% foetal bovine serum (Sigma-Aldrich). The cells were maintained in an incubator at 37 °C with the humidity set at 95% and 5% CO

_{2}and were transferred to T-25 culture flasks (Sarstedt Ltd., Wexford, Ireland) for irradiation. Three technical replicates of each of the cell lines were treated with each irradiation and experimental treatment as outlined here.

^{TM}automated colony counter (Oxford Optronics, Oxford, UK), with measurements of cell volume acquired using this instrument.

#### 4.1.2. FTIR Spectral Acquisition and Pre-Processing

^{−1}over the range 720–4000 cm

^{−1}with 128 scans per pixel. All data pre-processing steps were implemented in Python (v 3.9.12) using the OCTAVVS library for pre-processing [45]. Firstly, individual spectra were extracted from the images with outliers removed using Rosner’s test applied to the PC scores of spectra within a given class. The number of spectra in each class was down-sampled by a factor of 2 to improve computational efficiency. Subsequently spectra were corrected for atmospheric contributions and then scattering effects using the resonant-Mie scattering correction [46]. Spectra were smoothed using a Savitsky-Golay algorithm with an order of 5 and window of 15 points. Spectra were then truncated to the 800 cm

^{−1}to 4000 cm

^{−1}region. Finally, any residual baseline was removed using a concave rubber band algorithm and spectra were vector normalised. In totality these procedures resulted in a dataset of ~12,000 spectra for analysis.

#### 4.2. Chemometrics and Machine Learning

_{1}score as the metric of performance [48]. The following sections detail each of the methodologies which were employed.

#### 4.2.1. Principal Components Analysis

^{T}, removes the covariance between variables in the original data space with the reduction being performed by solving an eigenvalue-eigenvector problem on the covariance matrix of the data in its original space [26] as per Equation (1) (where T is the matrix of principal components scores and S is the diagonal eigenvalue matrix. Within biophotonics PCA has become one of the first options for recourse for researchers as the principal components can be readily interpreted via providing loadings which may be related to the original spectral variables.

#### 4.2.2. Support Vector Machine

_{1}, y

_{1}), (x

_{2}, y

_{2}),…, (x

_{m}, y

_{m}), are training data vectors x with class labels y where x

_{i}∈ R

^{d}denotes vectors in a d-dimensional feature space and y

_{i}∈ {−1, +1} is a class label [52], the SVM in its linear form finds the optimal separating margin by solving the following optimization task:

#### 4.2.3. t-SNE

_{i}and x

_{j}in a Cartesian coordinate system, into a conditional probability ${p}_{i|j}$. The probability density distribution of the neighbouring data points to x

_{i}are assumed as a Gaussian function centered at x

_{i}with a variance ${\sigma}_{i}$ such that the probability of x

_{j}to be selected as the neighbour of x

_{i}is given as [55]:

#### 4.2.4. Extreme-Gradient-Boosted Regression (XGBR)

#### 4.2.5. Classic Least Squares Spectral Fitting (CLS)

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Principal components analysis of (

**top**panel) PNT1A cell line and (

**bottom**panel) LNCaP cell line spectra. In each panel the left figure displays the cumulative explained variance and the right displays a pairs plot of the principal component scores for the first 5 principal components.

**Figure 3.**Representative t-SNE scores plots for (

**a**) PNT1A cells exposed to a range of treatment modes and (

**b**) LNCaP cells exposed to 2 Gy (IF) and 0 Gy (Control).

**Figure 4.**Performance of PCA-SVM versus principal component for (

**a**) PNT1A and (

**b**) LNCaP cell lines with variation in SVM hyperparameters.

**Figure 5.**Loadings to the first three principal components for (

**top**) analysis of PNT1A and (

**bottom**) LNCaP PCA. Specific loadings of interest are highlighted.

**Figure 6.**Examples of (

**i**) fitting of mean spectra and (

**ii**) CLS regression coefficients for (

**a**) PNT1A and (

**b**) LNCaP cell lines in which non-zero regression coefficients were observed (

**i**) PNT1A and (

**ii**) LNCaP cell lines in the fingerprint region using CLS regression. All regression coefficients have been normalised to the sham-irradiated (0 Gy) control for each cell line.

**Figure 7.**XGBoost regression of IR spectra from PNT1A cell line against cell volume. (

**a**) Association between spectral data and cell volume. (

**b**) Frequency with which spectral features (highlighted in red) are selected by XGBoost model in regression against cell volume.

**Table 1.**Results of testing via Welch’s ANOVA on CLS coefficients from fitting of PNT1A cell spectra.

F | p-Value | Molecule |
---|---|---|

3246 | <0.001 | Actin |

3836 | <0.001 | Cytochrome C |

4143 | <0.001 | Glycogen |

418 | <0.001 | IL8 |

2352 | <0.001 | Phosphatidyl-choline |

1531 | <0.001 | Phosphatidyl-inositol |

1006 | <0.001 | RNA |

336 | <0.001 | TGF-β2 |

1092 | <0.001 | Vitamin-C |

2657 | <0.001 | Vitamin-E |

**Table 2.**Results of post hoc pairwise testing with the Games-Howell approach on CLS coefficients from fitting of PNT1A cell spectra. Column A and B of the table identify the paired classes which are compared for each molecule, with SE denoting the standard error on the mean and T the t-statistic. Non-significant p-values at the level of p < 0.001 are highlighted in red.

A | B | SE | T | p-Value | Molecule |
---|---|---|---|---|---|

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 1.964 × 10^{−3} | −2.4 | 0.074 | Actin |

PNT1A 0 Gy | PNT1A OF | 1.713 × 10^{−3} | 32.4 | <0.001 | Actin |

PNT1A 0 Gy | PNT1A OF ICCM | 1.630 × 10^{−3} | −30.2 | <0.001 | Actin |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 3.004 × 10^{−2} | 6.4 | <0.001 | Cytochrome C |

PNT1A 0 Gy | PNT1A OF | 2.772 × 10^{−2} | −20.9 | <0.001 | Cytochrome C |

PNT1A 0 Gy | PNT1A OF ICCM | 2.255 × 10^{−2} | 42.9 | <0.001 | Cytochrome C |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 5.284 × 10^{−3} | 35.9 | <0.001 | Glycogen |

PNT1A 0 Gy | PNT1A OF | 7.196 × 10^{−3} | −73.6 | <0.001 | Glycogen |

PNT1A 0 Gy | PNT1A OF ICCM | 5.642 × 10^{−3} | 1.0 | 0.757 | Glycogen |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 2.950 × 10^{−2} | −0.2 | 0.997 | IL8 |

PNT1A 0 Gy | PNT1A OF | 2.188 × 10^{−2} | −16.9 | <0.001 | IL8 |

PNT1A 0 Gy | PNT1A OF ICCM | 3.463 × 10^{−2} | −33.0 | <0.001 | IL8 |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 4.661 × 10^{−3} | −16.7 | <0.001 | Phosphatidyl-choline |

PNT1A 0 Gy | PNT1A OF | 3.810 × 10^{−3} | 37.9 | <0.001 | Phosphatidyl-choline |

PNT1A 0 Gy | PNT1A OF ICCM | 3.966 × 10^{−3} | −17.7 | <0.001 | Phosphatidyl-choline |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 4.236 × 10^{−3} | 51.3 | <0.001 | Phosphatidyl-inositol |

PNT1A 0 Gy | PNT1A OF | 7.814 × 10^{−3} | −34.7 | <0.001 | Phosphatidyl-inositol |

PNT1A 0 Gy | PNT1A OF ICCM | 5.190 × 10^{−3} | 18.6 | <0.001 | Phosphatidyl-inositol |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 1.706 × 10^{−3} | 51.5 | <0.001 | RNA |

PNT1A 0 Gy | PNT1A OF | 1.721 × 10^{−3} | 12.1 | <0.001 | RNA |

PNT1A 0 Gy | PNT1A OF ICCM | 1.933 × 10^{−3} | 23.5 | <0.001 | RNA |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 1.507 × 10^{−3} | 11.5 | <0.001 | TGF-β2 |

PNT1A 0 Gy | PNT1A OF | 1.429 × 10^{−3} | −15.3 | <0.001 | TGF-β2 |

PNT1A 0 Gy | PNT1A OF ICCM | 1.486 × 10^{−3} | −5.6 | <0.001 | TGF-β2 |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 4.315 × 10^{−2} | −23.6 | <0.001 | Vitamin-C |

PNT1A 0 Gy | PNT1A OF | 2.655 × 10^{−2} | −33.8 | <0.001 | Vitamin-C |

PNT1A 0 Gy | PNT1A OF ICCM | 2.770 × 10^{−2} | 17.5 | <0.001 | Vitamin-C |

PNT1A 0 Gy | PNT1A 0 Gy ICCM | 7.249 × 10^{−3} | 23.2 | <0.001 | Vitamin-E |

PNT1A 0 Gy | PNT1A OF | 7.169 × 10^{−3} | −45.8 | <0.001 | Vitamin-E |

PNT1A 0 Gy | PNT1A OF ICCM | 9.688 × 10^{−3} | 43.5 | <0.001 | Vitamin-E |

**Table 3.**Results of testing via Welch’s ANOVA on CLS coefficients from fitting of LNCaP cell spectra.

F | p-Value | Molecule |
---|---|---|

1167 | <0.001 | Actin |

1180 | <0.001 | Cytochrome C |

3938 | <0.001 | Glycogen |

106 | <0.001 | IL8 |

272 | <0.001 | Phosphatidyl-choline |

7020 | <0.001 | Phosphatidyl-inositol |

389 | <0.001 | RNA |

1 | <0.001 | TGF-β2 |

5246 | <0.001 | Vitamin-C |

5833 | <0.001 | Vitamin-E |

**Table 4.**Results of post hoc pairwise testing with the Games-Howell approach on CLS coefficients from fitting of LNCaP cell spectra. Column A and B of the table identify the paired classes which are compared for each molecule, with SE denoting the standard error on the mean and T the t-statistic.

A | B | SE | T | p-Value | Molecule |
---|---|---|---|---|---|

LNCaP 0 Gy | LNCaP IF | 0.004 | 34.2 | <0.001 | Actin |

LNCaP 0 Gy | LNCaP IF | 0.112 | −34.4 | <0.001 | Cytochrome C |

LNCaP 0 Gy | LNCaP IF | 0.052 | −62.8 | <0.001 | Glycogen |

LNCaP 0 Gy | LNCaP IF | 0.064 | 10.3 | <0.001 | IL8 |

LNCaP 0 Gy | LNCaP IF | 0.006 | −16.5 | <0.001 | Phosphatidyl-choline |

LNCaP 0 Gy | LNCaP IF | 0.034 | −83.8 | <0.001 | Phosphatidyl-inositol |

LNCaP 0 Gy | LNCaP IF | 0.004 | 19.7 | <0.001 | RNA |

LNCaP 0 Gy | LNCaP IF | 0.004 | −1.1 | <0.001 | TGF-β2 |

LNCaP 0 Gy | LNCaP IF | 1.348 | −72.4 | <0.001 | Vitamin-C |

LNCaP 0 Gy | LNCaP IF | 0.135 | −76.4 | <0.001 | Vitamin-E |

**Table 5.**Colony volume measurements of PNT1A cell cultures (n = 3) from Shields et al (unpublished data) [5].

Irradiation | Volume Average (μm^{3}) | Std Dev |
---|---|---|

0 Gy | 699,592 | 105,269 |

Out of field (OF) | 345,629 | 192,621 |

0 Gy + ICCM | 514,930 | 83,311 |

Out of field + ICCM (OF + ICCM) | 1,062,630 | 254,959 |

Sample | Exposure Mode | Protein | Carbohydrate | RNA | Lipid | Cytokine | Antioxidants | Cytochrome C | DNA Damage | Cell Survival |
---|---|---|---|---|---|---|---|---|---|---|

PNT1A OF | Low dose | Decrease | Increase | No change | Increase | Increase | No change | Increase | Increase | Increase |

PNT1A OF ICCM | Low dose plus exposure to secreted factors | Increase | No change | Decrease | No change | No change | Decrease | Decrease | Increase | Increase |

PNTT1A ICCM | Exposure to secreted factors | No change | Decrease | Decrease | Increase | No change | Decrease | No change | No change | Decrease |

LNCAP 2 Gy | Exposure to high doses | Decrease | Increase | Decrease | Increase | Decrease | Increase | Increase | Increase | Not measured |

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## Share and Cite

**MDPI and ACS Style**

Slattery, C.; Nguyen, K.; Shields, L.; Vega-Carrascal, I.; Singleton, S.; Lyng, F.M.; McClean, B.; Meade, A.D.
Application of Advanced Non-Linear Spectral Decomposition and Regression Methods for Spectroscopic Analysis of Targeted and Non-Targeted Irradiation Effects in an *In-Vitro* Model. *Int. J. Mol. Sci.* **2022**, *23*, 12986.
https://doi.org/10.3390/ijms232112986

**AMA Style**

Slattery C, Nguyen K, Shields L, Vega-Carrascal I, Singleton S, Lyng FM, McClean B, Meade AD.
Application of Advanced Non-Linear Spectral Decomposition and Regression Methods for Spectroscopic Analysis of Targeted and Non-Targeted Irradiation Effects in an *In-Vitro* Model. *International Journal of Molecular Sciences*. 2022; 23(21):12986.
https://doi.org/10.3390/ijms232112986

**Chicago/Turabian Style**

Slattery, Ciara, Khanh Nguyen, Laura Shields, Isabel Vega-Carrascal, Sean Singleton, Fiona M. Lyng, Brendan McClean, and Aidan D. Meade.
2022. "Application of Advanced Non-Linear Spectral Decomposition and Regression Methods for Spectroscopic Analysis of Targeted and Non-Targeted Irradiation Effects in an *In-Vitro* Model" *International Journal of Molecular Sciences* 23, no. 21: 12986.
https://doi.org/10.3390/ijms232112986