# Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos

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^{†}

## Abstract

**:**

## 1. Introduction

^{+}, and proteases, towards extracellular space [9,10]. Since the resulting acidification and proteolytic remodeling of the tumor microenvironment drives invasion, there is hope that inhibition of excessive lysosomal exocytosis could limit cancer metastasis [11,12].

## 2. Materials and Methods

#### 2.1. Cell Culture, Nanoparticle Treatments, and Confocal Microscopy

^{−1}gentamycin. MCF-10A cells were cultured in DMEM/F12 (11330-032, Thermo Fisher Scientific, Waltham, MA, USA) with 5% horse serum, 20 ng mL

^{−1}epidermal growth factor, 10 µg mL

^{−1}insulin, 0.5 mg mL

^{−1}hydrocortisone, 100 ng mL

^{−1}cholera toxin, and penicillin/streptomycin (10,000 U mL

^{−1}penicillin and 10,000 µg mL

^{−1}streptomycin). MCF-7 were cultured in RPMI with 10% FBS and 25 μg mL

^{−1}gentamycin. MCF-10A, MCF-7, HT-1080 and MEF cells were cultured in a 5% CO

_{2}atmosphere at 37 °C. MDA-MB-231 were cultured in L-15 medium (21083027, Thermo Fisher Scientific, Waltham, MA, USA) with 10% FBS and 25 μg mL

^{−1}gentamycin at 37 °C without CO

_{2}. All cell lines used in this study were free of mycoplasma.

_{H}≈ 7.8 nm (from DLS).

^{−1}). Subconfluent cells were then cultured without NPs (Control/no-NPs), or continuously exposed to 80:20 or TMA NPs (50 nM) for 8 h (for HT-1080 and MEF), or 24 h (for MCF-10A, MDA-MB-231 and MCF-7) at 37 °C. The NP concentrations/exposure times were chosen to allow NP aggregation inside cells’ lysosomes but not induce cell death during lysosome tracking experiments. Overall, at higher concentrations and/or longer exposure times, TMA NPs are toxic, while 80:20 NPs are selectively cytotoxic only towards cancer cells. A detailed description of the cell responses is provided in [37]. Both cancer and noncancerous cells readily internalized both types of nanoparticles, though 80:20 nanoparticles aggregated more readily in lysosomes than TMAs. NP clusters—larger in cancer cells and smaller in noncancerous cells—were imaged label-free with confocal reflection microscopy as described previously [37,47].

_{2}concentrations maintained using a stage-fitted incubator and gas mixer (Live Cell Instruments, Seoul, Korea) as described previously [37,47].

#### 2.2. Image Processing and Tracking

#### 2.3. Movement Analysis

#### 2.3.1. Continuous Wavelet Transform

#### 2.3.2. Active Transport Detection

#### 2.3.3. Co-Movement Detection

#### 2.4. Statistical Data Analysis

## 3. Results

#### 3.1. Lysosomal Movements Are Characterized by a Heavy-Tailed, Lognormal Distribution of Run/Flight Lengths

#### 3.2. Tissue Origin and Cancer-Specific Differences in Lysosomal Dynamics

#### 3.3. Wavelet-Based Approach for Detection of Lysosome-Nanoparticle Co-Movement

#### 3.4. Mixed-Charge Gold Nanoparticles Selectively Disrupt Lysosomal Transport in Cancer Cells

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**CCDFs of datasets with corresponding distribution fits. Subpanels show curves for run (

**a**–

**c**,

**g**,

**h**) and flight (

**d**–

**f**,

**i**,

**j**) lengths for MCF-10A (

**a**,

**d**), MDA-MB-231(

**b**,

**e**), MCF-7 (

**c**,

**f**), MEF (

**g**,

**i**), and HT1080 (

**h**,

**j**) cells. Data CCDF curves are in burgundy dotted lines; best-fit distributions are plotted in solid lines, while competing distributions are in dashed lines.

**Figure A2.**The effect of nanoparticle cargos on the average run (

**a**) and flight (

**b**) lengths. The notation of the box plots and experimental source data are identical to the main-text Figure 4 and Figure 5. Asterisk or ‘ns’ indicated in the lower part of the plots indicate presence or absence of statistically significant differences, respectively, between parameters for lysosomes with or without cargos determined with two-tailed paired Student’s t test (* p < 0.05). Similarly, asterisk or ‘ns’ above the box plots indicate statistical significance of the difference between lysosomes from cells treated with NPs (white and grey boxes) versus all lysosomes in untreated, control cells (colored boxes) determined using Wilcoxon–Mann–Whitney test (* p < 0.05). The analyses were based on the following number of cells and lysosome trajectories: MCF-10A/Control (n = 8 cells, l = 5260 lysosome trajectories); MCF-10A/80-20 (n = 10): NP− (l = 4177), NP+ (l = 597); MCF-10A/TMA (n = 12): NP− (l = 3769), NP+ (l = 303); MDA-MB-231/Control (n = 4, l = 1076); MDA-MB-231/80-20 (n = 17): NP− (l = 2771), NP+ (l = 260); MDA-MB-231/TMA (n = 14): NP− (l = 1618), NP+ (l = 116); MEF/Control (n = 5, l = 5781); MEF/80–20 (n = 6): NP− (l = 6272), NP+ (l = 131); MEF/TMA (n = 3): NP− (l = 5304), NP+ (l = 36); and HT-1080/Control (n = 8, l = 7953); HT/80–20 (n = 11): NP− (l = 4294), NP+ (l = 304); HT/TMA (n = 4): NP− (l = 2283), NP+ (l = 79).

**Figure A3.**The effect of nanoparticle treatment on lysosomal motion parameters for MCF-7 cells. for all lysosomes from each cell were pooled together to compute (

**a**) exponent $\alpha $ and (

**b**) diffusion coefficient D, (

**c**) percentage of time spent in active transport, and (

**d**,

**e**) average run and flight lengths. For more details, see Figure 4 caption. Asterisk or ‘ns’ indicated in the lower part of the plots indicate presence or absence of statistically significant differences, respectively, between parameters for lysosomes with or without cargos determined with two-tailed paired Student’s t test (* p < 0.05). Similarly, asterisk or ‘ns’ above the box plots indicate statistical significance of the difference between lysosomes from cells treated with NPs (white and grey boxes) versus all lysosomes in untreated, control cells (colored boxes) determined using Wilcoxon–Mann–Whitney test (* p < 0.05). Number of cells and trajectories used: Control (n = 4 cells, l = 1756 lysosome trajectories); 80–20 (n = 4): NP− (l = 369), NP+ (l = 31).

## Appendix B

**Table A1.**Distributions used in model comparison. Here, $x$ is observed data, $a$ is the minimal data point, $\mathsf{\Gamma}$ is upper incomplete gamma function, $erfc$ is complementary error function, and $\mu ,\lambda ,\sigma ,\beta $ are parameters of the corresponding distributions.

Distribution Name | Probability Density Function p(x) |
---|---|

Power law | $\frac{{x}^{-\mu}}{{a}^{1-\mu}}\left(\mu -1\right)$ |

Truncated power law | ${x}^{-\mu}{e}^{-\lambda x}\frac{{\lambda}^{1-\mu}}{\mathsf{\Gamma}\left(1-\mu ,\lambda a\right)}$ |

Log-normal | $\frac{1}{x}\mathrm{exp}\left[-\frac{{\left(\mathrm{ln}x-\mu \right)}^{2}}{2{\sigma}^{2}}\right]\sqrt{\frac{2}{\pi {\sigma}^{2}}}{\left[\mathrm{erfc}(\frac{a-\mathsf{\mu}}{\sqrt{2}\sigma})\right]}^{-1}$ |

Stretched exponential | $\beta \lambda {x}^{\beta -1}{e}^{\lambda \left({a}^{\beta}-{x}^{\beta}\right)}$ |

Exponential | $\mathsf{\lambda}{e}^{\mathsf{\lambda}\left(a-x\right)}$ |

**Table A2.**Lysosomal diameters in all cell types. Lysosome sizes in all cell types analyzed in the present study without or with 80:20 NP treatment were quantified from confocal midplane images of Lysotracker-stained organelles. Data = mean ± s.d. A two-tailed Student’s t-test with unequal variances between control and NP-treated groups. * p < 0.05;

^{ns}= not significant. Data are from Borkowska et al., 2020 [37].

Cell Type/Treatment | Lysosomal Diameter [μm] | Lysosomes, l | Cells, n |
---|---|---|---|

MEF | 0.65 ± 0.23 | 525 | 7 |

MEF + 80:20 NPs | 0.71 ± 0.25 * | 759 | 6 |

HT-1080 | 0.67 ± 0.24 | 707 | 6 |

HT-1080 + 80:20 NPs | 0.99 ± 0.34 * | 539 | 11 |

MCF-10A | 0.54 ± 0.20 | 316 | 10 |

MCF-10A + 80:20 NPs | 0.57 ± 0.22 ^{ns} | 340 | 12 |

MDA-MB-231 | 0.67 ± 0.30 | 418 | 16 |

MDA-MB-231 + 80:20 NPs | 1.00 ± 0.49 * | 235 | 10 |

MCF-7 | 0.80 ± 0.35 | 250 | 11 |

MCF-7 + 80:20 NPs | 1.42 ± 0.92 * | 239 | 11 |

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**Figure 1.**Schematic of the analysis of lysosome movement patterns and lysosome-nanoparticle co-transport. (

**a**) A snapshot of a time-series of an MCF-10A cell with lysosomes marked by Lysotracker Red and imaged with fluorescence and gold nanoparticle aggregates (Au NPs) imaged label-free in confocal reflection mode (CRM). See also Supplementary Movies S1 and S2. (

**b**) Both lysosomes and Au NP aggregates are tracked by a single-particle tracking module in NIS-Elements software. (

**c**) Multiscale wavelet coefficients are computed by continuous wavelet transform (CWT) for x and y coordinates of trajectories. (

**d**) Shows an example of lysosome trajectory segmented using CWT-based active transport detection. The color indicates intervals of diffusive motion (grey) and directional, active transport—several “runs” (colored) that often join to form directional “flights” (dashed lines connect the beginnings with ends of such flights). (

**e**) CWT results are also used to detect co-transported lysosomes and Au NP aggregates. (

**f**) Classifications performed by the previous stages of the workflow are used in the statistical data analysis, investigating lysosome mean square displacements (MSD) and persistence lengths for runs (l) and flights (L). See the Section 2 for more details.

**Figure 2.**Lysosome movements are superdiffusive and fit the lognormal distribution. (

**a**) Log-log plots of the lysosomes’ mean square displacements (MSD) versus time, MSD ∝ t

^{α}, with all trajectories for all cells from one type pooled together where α > 1 indicates superdiffusive lysosome movements for all cell types. See Supplementary Movie S1. Box-plots showing (

**b**) exponent α and (

**c**) diffusion coefficient, D, and (

**d**) % time spent in active motion. Data are displayed as box-and-whisker plots; boxes delineate the lower and upper quartiles of the data, middle lines show median values, dashed lines show mean values for each cell type, colored dots are data points for each analyzed cell, and whiskers show upper and lower extremes. For (

**b**–

**d**), all trajectories in each analyzed cell were pooled together, and mean values for each cell were computed. The latter are shown as data points in the box plots. MCF-10A (n = 8 cells, l = 5260 lysosome trajectories), MDA-MB-231 (n = 4, l = 1076); MCF-7 (n = 4, l = 1756), MEF (n = 5, l = 5781), and HT-1080 (n = 8, l = 7953). (

**e**–

**h**) The complementary cumulative distribution functions, CCDFs, for run and flight lengths detected with wavelet analysis and plotted on a log-log scale; insets highlight the difference on a linear scale, which otherwise is not as apparent in this region of the logarithmically scaled plots. Noncancerous breast epithelial MCF-10A cell line is compared against MDA-MB-231 and MCF-7 breast adenocarcinomas. Mouse embryonic fibroblasts (MEF) are compared against the HT-1080 fibrosarcoma cell line. Asterisk denotes statistically significant differences between run/flight lengths for cancer cells compared with noncancerous counterparts determined by a Cramer–von Mises criterion (* p < 0.01). Only the significant differences are shown. The number of cells and runs/flights analyzed were as follows: MCF-10A (r = 5742 runs, f = 4830 flights), MDA-MB-231 (r = 1683, f = 1384), MCF-7 (r = 3410, f = 2829), MEF (r = 6156, f = 5060), and HT-1080 (r = 8697, f = 7189). The statistical parameters are shown in Table 1, and model fits are shown in Figure A1.

**Figure 3.**Examples of classification by the co-movement detection method. Lysosome–NP cluster pairs are correctly classified as moving together (

**a**–

**d**) and separately (

**d**–

**f**). (

**a**,

**d**) are lysosome (red) and NP-aggregate (green) experimental images prepared by combining images from the corresponding microscope channels. Arrows indicate the objects from the analyzed pair; the scale bars are $1\mathsf{\mu}\mathrm{m}$. (

**b**,

**e**) are center-to-center distances of the pairs. (

**c**,

**f**) demonstrate CWT coefficient maps for trajectories’ x-axes. Inset box with ${P}_{x}$ values show the Pearson’s correlation coefficient between lysosomal and NPs-aggregate CWT coefficient maps. For clarity, data only from the 0-70 s time interval (out of 300 s) are shown on (

**e**,

**f**). See Supplementary Movie S2.

**Figure 4.**Cell type-specific effects of nanoparticle cargos on lysosome movement parameters. MCF-10A non-cancerous breast epithelial cells vs. MDA-MB-231 breast adenocarcinoma and normal mouse embryonic fibroblasts (MEF) vs. HT-1080 fibrosarcoma were untreated (Control), or treated with mixed-charge 80:20 or purely cationic TMA NPs. Trajectories for all lysosomes from each cell were pooled together to compute (

**a**) exponent $\alpha $ and (

**b**) diffusion coefficient D. For NP-treated samples, wavelet-based co-movement algorithm (see Materials and Methods) was used to further subdivide lysosomes into those carrying NP cargos (Lyso NP+) and those without detectable NP cargos (Lyso NP−). Data are displayed as box-and-whisker plots; boxes delineate the lower and upper quartiles of the data, middle lines show median values, dashed lines show mean vales, colored dots show lysosome dynamics parameters for each cell and whiskers show upper and lower extremes. Asterisk or ‘ns’ indicated in the lower part of the plots indicate presence or absence of statistically significant differences, respectively, between parameters for lysosomes with or without cargos determined with two-tailed paired Student’s t test (* p < 0.05). Similarly, asterisk or ‘ns’ above the box plots indicate statistical significance of the difference between lysosomes from cells treated with NPs (white and grey boxes) versus all lysosomes in untreated, control cells (colored boxes) determined using Wilcoxon–Mann–Whitney test. (* p < 0.05). The analyses were based on the following number of cells and lysosome trajectories: MCF-10A/Control (n = 8 cells, l = 5260 lysosome trajectories); MCF-10A/80-20 (n = 10): NP− (l = 4177), NP+ (l = 597); MCF-10A/TMA (n = 12): NP− (l = 3769), NP+ (l = 303); MDA-MB-231/Control (n = 4, l = 1076); MDA-MB-231/80-20 (n = 17): NP− (l = 2771), NP+ (l = 260); MDA-MB-231/TMA (n = 14): NP− (l = 1618), NP+ (l = 116); MEF/Control (n = 5, l = 5781); MEF/80–20 (n = 6): NP− (l = 6272), NP+ (l = 131); MEF/TMA (n = 3): NP− (l = 5304), NP+ (l = 36); and HT-1080/Control (n = 8, l = 7953); HT/80–20 (n = 11): NP− (l = 4294), NP+ (l = 304); HT/TMA (n = 4): NP− (l = 2283), NP+ (l = 79).

**Figure 5.**The effect of nanoparticle cargos on lysosome active transport. Time spent in active transport was computed after identifying active and passive trajectory segments with a wavelet-based approach. Note that for NP-treated samples, a wavelet-based co-movement algorithm (see Materials and Methods) was used to further subdivide lysosomes into those carrying NP cargos (Lyso NP+) and those without detectable cargos (Lyso NP−). Asterisk or ‘ns’ indicated in the lower part of the plots indicate presence or absence of statistically significant differences, respectively, between parameters for lysosomes with or without cargos determined with two-tailed paired Student’s t test (* p < 0.05). Similarly, asterisk or ‘ns’ above the box plots indicate statistical significance of the difference between lysosomes from cells treated with NPs (white and grey boxes) versus all lysosomes in untreated, control cells (colored boxes) determined using Wilcoxon–Mann–Whitney test. (* p < 0.05). All experimental details, statistical tests, and numbers of trajectories and cells analyzed are identical to Figure 4.

**Table 1.**Statistical analysis of lysosome movements in cancer and noncancerous cells. The exponent α and diffusion coefficient D values were computed from mean square displacement (MSD) versus time plots shown in Figure 2a. Data = mean ± s.d. n = 4–8 cells (see below). The fit parameters for run and flight lengths—from lognormal (or stretched exponential where appropriate) distributions—and Akaike weights for all model comparisons are shown (see Section 2 for details). LN = lognormal, P = power law, TP = truncated power law, SE = stretched exponential, E = exponential. The strongest supported model is indicated in bold. Complementary cumulative distribution functions (CCDFs) for run (l) and flight (L) lengths shown in Figure 2e–h for all cell types fit lognormal distributions, except MCF-10A for which the CCDF for L fits stretched exponential distribution. See also Figure A1 for model fits. The number of cells and lysosome trajectories analyzed were as follows: MCF-10A (n = 8 cells, l = 5260 lysosome trajectories), MDA-MB-231 (n = 4, l = 1076), MCF-7 (n = 4, l = 1756), MEF (n = 5, l = 5781), and HT-1080 (n = 8, l = 7953).

Cell Type | MSD (a) | D (μm ^{2}/s)
| Fit Parameters | Akaike Weights | ||||
---|---|---|---|---|---|---|---|---|

LN | P | TP | SE | E | ||||

MCF-10A | 1.29 ± 0.05 | 0.022 ± 0.004 | Runs: μ = −0.193; σ = 0.804 Flights: λ = 0.840; β = 1.037 | 10 | 0 <0.01 | <0.01 <0.01 | <0.010.83 | <0.01 0.17 |

MDA-MB-231 | 1.31 ± 0.05 | 0.029 ± 0.006 | Runs: μ = −0.147; σ = 0.833 Flights: μ = 0.028; σ = 0.838 | 0.991 | <0.01 <0.01 | <0.01 <0.01 | <0.01 <0.01 | <0.01 <0.01 |

MCF-7 | 1.35 ± 0.04 | 0.029 ± 0.010 | Runs: μ = −0.013; σ = 0.834 Flights: μ = 0.151; σ = 0.838 | 11 | 0 0 | 0 <0.01 | <0.01 <0.01 | <0.01 <0.01 |

MEF | 1.36 ± 0.09 | 0.018 ± 0.003 | Runs: μ = −0.175; σ = 0.856 Flights: μ = −0.155; σ = 0.929 | 10.99 | 0 0 | <0.01 <0.01 | <0.01 <0.01 | <0.01 <0.01 |

HT-1080 | 1.34 ± 0.06 | 0.015 ± 0.003 | Runs: μ = −0.183; σ = 0.802 Flights: μ = −0.019; σ = 0.829 | 11 | 0 0 | 0 0 | <0.01 <0.01 | <0.01 <0.01 |

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Polev, K.; Kolygina, D.V.; Kandere-Grzybowska, K.; Grzybowski, B.A. Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos. *Cells* **2022**, *11*, 270.
https://doi.org/10.3390/cells11020270

**AMA Style**

Polev K, Kolygina DV, Kandere-Grzybowska K, Grzybowski BA. Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos. *Cells*. 2022; 11(2):270.
https://doi.org/10.3390/cells11020270

**Chicago/Turabian Style**

Polev, Konstantin, Diana V. Kolygina, Kristiana Kandere-Grzybowska, and Bartosz A. Grzybowski. 2022. "Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos" *Cells* 11, no. 2: 270.
https://doi.org/10.3390/cells11020270