# Toxicity assessment of titanium dioxide nanoparticles on microorganisms through topological data analysis of high dimensional single-cell nanomechanical data

M. Offroy, Ludovic Duponchel, A. Razafitianamaharavo, C. Pagnout, J. F. L. Duval

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## ► To cite this version:

M. Offroy, Ludovic Duponchel, A. Razafitianamaharavo, C. Pagnout, J. F. L. Duval. Toxicity assessment of titanium dioxide nanoparticles on microorganisms through topological data analysis of high dimensional single-cell nanomechanical data. Talanta, 2025, Talanta, 286, pp.127482. 10.1016/j.talanta.2024.127482. hal-04893221

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# Toxicity assessment of titanium dioxide nanoparticles on microorganisms through topological data analysis of high dimensional single-cell nanomechanical data

Marc Offroy<sup>a,∗</sup> <sup> ID </sup>, Ludovic Duponchel<sup>b</sup> <sup> ID </sup>, Angelina Razafitianamaharavo<sup>a</sup>, Christophe Pagnout<sup>c</sup>, Jérôme F.L. Duval<sup>a ID</sup>

## ARTICLE INFO

Handling Editor: Prof. J. Wang

### Keywords:

Toxicity assessment

Nanoparticles

Topological data analysis

Atomic force microscopy

Biomechanics

Imaging

Data mining

## ABSTRACT

There is a growing interest in the development of methods for the detection of nanoparticle (NP) toxicity to living organisms based on the analysis of relevant multidimensional data sets. In particular the detection of preliminary signs of NPs toxicity effects would benefit from the selection of data featuring NPs-induced alterations of biological barriers. Accordingly, we present an original Topological Data Analysis (TDA) of the nanomechanical properties of *Escherichia coli* cell surface, evaluated by multiparametric Atomic Force Microscopy (AFM) after exposure of the cells to increasing concentrations of titanium dioxide nanoparticles (TiO₂NPs). Topological networks are generated from spatially resolved multidimensional nanomechanical cell data consisting of elastic moduli, turgor pressures and AFM tip indentations of the biosurface. The topological networks reflect the resistance/sensitivity of cells to TiO₂NPs as a function of cell surface phenotype, and the methodology further highlights heterogeneities in response at the single cell and multi-individual levels. Overall, the method provides an efficient approach to assess nanoparticle toxicity without requiring prior knowledge, while naturally accounting for variability in cellular response at different scales.

## 1. Introduction

The reactivity of nanoparticles (NPs) depends on their size and the large surface area they develop when dispersed in aquatic media [1,2]. Nonetheless, forecasting the toxicity of NPs on living cells on the basis of NPs descriptors is greatly constrained. This limitation arises from significant variability in the physicochemical properties of native NPs, their alterations during cell exposure (e.g., bio-corona or eco-corona acquisition), the establishment of cell resistance mechanisms, and the broad spectrum of scales across which NPs-induced adverse effects might -or might not- occur, from the single cell, the cell (sub)population (in vitro) to the whole organism (in vivo) [3-5]. Although the use of animal models in toxicology may mimic the response expected in humans, the cost and delay required to conduct such experiments, as well as the related ethical issues can seriously limit the approach. As a result, the assessment of toxic effects using standardized in vitro assays or analysis of dose-response relationships with cell mortality or cell

growth inhibition as toxicity endpoints have become popular despite of recognized limitations [6-8]. In parallel, the development of alternative computational strategies for predicting/identifying NPs properties leading to toxicity effects on (micro)organisms made significant progress, e.g., regression methods [9], decision trees [10] or artificial neural networks [11].

However, many of these in vitro approaches and related numerical toxicity tests, though important for risk assessment, suffer from severe limitations, namely: (i) The outcome of developed computational approaches depends inherently on the initial (arbitrary) choice made for the physicochemical descriptors of the nanoparticles (e.g., size, shape, zeta potential, chemical composition, or crystallinity [12]) and, more specifically, bias may be generated by their possible multicollinearity [13]. To illustrate, the historical Derjaguin-Landau-Verwey-Overbeek (DLVO) theory has long established that the stability of (nano)particles against aggregation depends strongly on their electrostatic surface properties [14]. However, the latter cannot be systematically converted

<footnote><sup>a</sup> Université de Lorraine, CNRS, LIEC, F-54000, Nancy, France</footnote>

<footnote><sup>b</sup> Univ. Lille, CNRS, UMR 8516, LASIRE-Laboratoire avancé de spectroscopie pour les interactions, la réactivité et l'environnement, F-59000, Lille, France</footnote>

<footnote><sup>c</sup> Université de Lorraine, CNRS, LIEC, F-57000, Metz, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: marc.offroy@univ-lorraine.fr (M. Offroy).</footnote>
into conventional zeta potential, depending on the hydrodynamic softness of the NPs analysed [15]. In addition, reported predictive computational methods applied to the assessment of NPs toxicity to organisms may differ according to the nature of the biological endpoint considered, for example, cell viability, oxidative stress or proxies for inflammatory response [16]. As a result, the respective "predictable character" of these various methods is far from clear, especially as there is controversy over the molecular origins of the mechanisms driving toxicity (e.g., oxidative versus osmotic stresses) and their relative significance [8,17]. (ii) The inherent influence of measurement conditions (e.g., salinity, pH, nature of the ions in the exposome, temperature, etc.) on the physicochemical properties of the NPs selected as toxicity descriptors is either overlooked or investigated at the margin [18,19]. The nature and magnitude of NPs-induced stress on living (micro)organisms may further differ depending on factors such as medium composition, cell physiology, membrane surface phenotype, amount of bioavailable energetic resources or even on the setting of stress-mitigation strategies like cell vesiculation [8,18,19]. In addition, the mechanistic assessment of NPs-cell interactions and biological implications thereof for predicting toxicity further remains a necessary but not sufficient condition, as evidenced by many studies demonstrating a lack of clear connection between various NP descriptors and cell response [20]. These elements strongly limit the claimed predictability of numerical strategies based on NP descriptors for identifying or qualifying the hazardous potential of nanoparticles. (iii) Last, to the best of our knowledge, there is currently no straightforward numerical method capable of describing, "simply" and without prior knowledge, the occurrence and strength of NPs-induced toxicity effects from a reduction and practical representation of high dimensional data. Clearly, the challenge resides in the mathematical handling of big datasets, which is essential to capture the multifaceted and multiscale origins of the intricate biophysicochemical processes that contribute to NPs toxicity for a given organism.

To address the limitations outlined in points (i) to (iii) above, this article reports an original method based on Topological Data Analysis (TDA) and Atomic Force Microscopy (AFM) to detect the occurrence of detrimental impacts caused by Titanium dioxide nanoparticles (TiO₂NPs) on *Escherichia coli* (*E. coli*) bacteria. The selection of TiO₂NPs is motivated by the worldwide production of these NPs, and their use in many industrial sectors and everyday life products (cosmetics, textiles, drugs, paints, pharmaceuticals, foods, cars, etc.) [12,21–24]. The choice of *E. coli* as model bacteria stems is due to the availability of a commercially available genome-wide gene knockout mutant library, which allow the use of mutants with different surface phenotypes [8,17, 25]. The data analysed using TDA to assess TiO₂NPs toxicity pertains to the nanomechanical properties of cells that qualify the integrity and alterations of *E. coli* surface when exposed to varying concentrations of TiO₂NPs [8]. Our choice of cell nanomechanics as a marker to monitor the effects of TiO₂NPs is motivated by its central role in cell survival and proliferation, cell physiology, and cell resistance to a variety of stressors [26–30]. Thus, this work provides the first proof of concept for the feasibility of the TDA-AFM method in the field of nanoparticle toxicology assessments, with potential applications of the method to toxins and contaminants other than nanoparticles (see Fig. 1).

# 2. Material and method

## 2.1. Bacterial culture and preparation

The protocols adopted for bacterial culture and preparation are detailed in Pagnout et al. [8] and are recalled here for the sake of completeness. The knock-out *E. coli* *rfa*-gene mutants (or deep-rough mutants) were obtained from the Coli Genetic Stock Center, Yale University. The selected *E. coli* K12 *rfa*-mutants express O-antigen-free lipopolysaccharides (LPS) with distinct inner or outer core compositions. More specifically, the deep-rough mutants JW3606 (*ΔrfaG*) and JW3596 (*ΔrfaC*) selected in this work lack the outer core LPS component and

differ according to the presence or absence of heptose units in the inner core [8,17,31] (Fig. 2). Knock-out mutations were verified by PCR before freezing at -80 °C in 50 % glycerol solution.

For experiments, cell cultures were first streaked from frozen stock on lysogeny broth (LB) agar (LB broth containing 1.5 w/v % agar) and incubated at 37 °C. Then, 4 mL of preculture LB medium was inoculated with an isolated colony and incubated overnight at 37 °C under stirring. The next day, 100 mL of M9 medium broth (6 g/L Na₂HPO₄, 3 g/L KH₂PO₄, 1 g/L NH₄Cl, 0.5 g/L NaCl, 1 mM MgSO₄, 0.1 mM CaCl₂, 0.2 % glucose, 10 µg/mL thiamine, 20 µg/mL proline, 25 µg/mL uridine) were seeded with the precultured cells at 1:100 dilution and incubated at 37 °C and 150 rpm until growth exponential phase was reached (OD₆₀₀nm-0.5). The cells were then harvested by centrifugation (5000×g, 5 min) and washed twice with 10 mM KNO₃. OD₆₀₀nm of the obtained bacterial suspensions was finally adjusted to a final value of 0.5 in 10 mM KNO₃. All bacterial cultures were supplemented with kanamycin (30 mg/L) as selective pressure.

## 2.2. Titanium dioxide nanoparticles

Aeroxide P25 TiO₂ nano-powder was purchased from Evonik Degussa GmbH (Frankfurt, Germany). TiO₂ nanoparticles have an 80:20 anatase:rutile composition and are defined by a pristine particle radius of ca. 21 nm and a specific surface area of 50 ± 15 m²/g. Suspensions of TiO₂NPs were prepared by dispersing 100 mg of nanopowder in 10 mL of sterile ultrapure water (Milli-Q water, 18.2 MΩ cm), followed by probe sonication (Sonics Vibra-cell 750 W, Sonics & Materials, frequency 20 kHz, 3 mm micro tip, amplitude 40 %) for 30 min at 4 °C in the dark to break up large TiO₂NPs aggregates and for homogenization purposes. The so-prepared stock suspension of TiO₂NPs (10 g/L concentration) was stable against aggregation-sedimentation for one month, and was protected from light.

## 2.3. Atomic Force Microscopy measurements

The Atomic Force Microscopy (AFM) measurements considered here for TDA-based detection of TiO₂NPs toxicity to *rfa*-gene *E. coli* mutants are detailed in Pagnout et al. [8]. The measurement procedure is recalled below for clarity purpose. The two deep-rough mutants were exposed to 0, 1, 2, 5, 10 and 20 mg/L TiO₂NPs (labelled NPO, NP1, NP2, NP5, NP10 and NP20) at pH~5.5-6 under agitation conditions for 20 h in the dark at 20 °C. For each concentration, 8 drops of cells suspension (i.e., from the same or different colonies) were first deposited on a cleaned borosilicate glass slide, which was previously covered by a layer of polyethyleneimine (PEI) (Sigma, Mw = 750,000 g/mol) upon immersion in 0.1 % PEI solution during 30 min. The glass slide was then rinsed with 1 mM KNO₃ solution to remove unbound or loosely bound bacteria from the surface. The live bacteria attached on the surface were then maintained in a 1 mM KNO₃ environment during AFM experiments performed at ambient temperature and natural pH. AFM measurements were performed using a FastScan Dimension Icon with Nanoscope V controller (Bruker) operating in PeakForce tapping mode in liquid medium. This mode has the advantage of simultaneously providing both cell surface images with resolution of about 20 nm (size of the hemispherical AFM probe tip) and load force measurements as a function of the AFM probe-to-cell surface separation distance. The AFM probes used were NPG Silicon Nitride probes (NPG-10, Bruker Corporation) with a cantilever spring constant of 0.40 ± 0.2 N/m determined as described in Butt et al. [32]. Force curves were systematically measured at the apex area of the bacterial cells to minimize convolution between probe geometry and sample surface topography. Prior to each experiment, the deflection sensitivity was determined from measurement on a hard substrate and the thermal tuning method was adopted for refined evaluation of the cantilever spring constant. Force versus indentation curves were then derived from raw data (i.e., cantilever deflection [nm] versus vertical piezo position [nm]) collected during the approach of the
<figure><img src="image_4.png" /><figcaption>Fig. 1. Principles of the TDA-AFM method for the toxicological evaluation of TiO₂NPs on E. coli.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 2. The deep rough mutants JW3606 and JW3596 feature LPS components that differ according to the presence or absence of heptose units in the inner core.</figcaption></figure>

AFM probe to the bacterial surface.

This raw AFM data was recorded pixel by pixel at the centre of the cell surface with a scan size of 500 nm at a scan rate of 1 Hz and a probe velocity displacement of 1 µm/s, corresponding to 256 × 256 local force measurements on the investigated cell surface area. As a result, 65536 force curves were generated on 500 × 500 nm² surface area of a single cell, and their analysis was performed according to the nanomechanical model and numerical methodology detailed in Offroy et al. [30]. Briefly, the home-made MATLAB program elaborated for AFM force curves analysis is able to evaluate, in a robust and fast manner, the defining nanomechanical properties (E, kcell) and the indentation δ* (Fig. S1 in Appendix A, Supplementary Material) on the basis of Sneddon model corrected for finite cell thickness and Hook's law [33].

## 2.4. Topological data analysis (TDA)

Following the development of high-performance mathematical tools capable of handling data without oversimplification of system complexity, Topological Data Analysis (TDA) aims to develop and optimize a new data analysis approach derived from a mathematical discipline: topology. The originality of topology is that it uses tools to study the shapes of data [34]. Historically, mathematicians have illustrated the benefits of topology on abstract shapes, and applications on data of practical interest have emerged [35,36]. It is only recently that TDA has been formulated, notably through the pioneering work from G. Carlsson [37–39]. The objective of TDA is to visualize and interpret big data sets by defining an equivalent and simpler representation (i.e., graphical method) whose “meaning” is related to the problem to be solved. This concept has already been successfully applied in various disciplinary fields, including oncology to identify subpopulations affected by breast cancer [40] or to address the role of CD8 and CD4

T-cells (lymphocytes) in type I and type II diabetes [41], but also in more exotic topics such as identifying profiles of NBA basketball players [38]. Likewise, TDA results obtained in vibrational spectroscopy are extremely promising compared to conventional chemometric tools [42].

The TDA algorithm consists of four main steps: (i) projection of the data in the Euclidean space, (ii) analysis of the relevant Euclidean distances between data points using a mathematical function comparable to a “lens” with which intervals are created, (iii) analysis of each interval by a single-linkage clustering algorithm [43] in order to find the future nodes of the topological network. The default colour of a node is the average “lens” value applicable for the interval where the cluster is found, while the node size is proportional to the number of data points in the cluster. Finally, (iv) generate the topological network. The TDA algorithm requires two meta-parameters to operate, which determine the resolution of the generated network, namely the interval length and the percentage of overlap between. Unlike classical topology, where nodes are connected according to a distance criterion, TDA allows nodes to be connected in a more generic way according to a logical relationship defined by the “lens” [43]. In fact, nodes are interconnected if and only if the corresponding clusters share data points, with the degree of connection determined by the specified overlap percentage. Advantage of TDA is its adaptability since one or more mathematical functions serving as “lens(es)” can be employed, in parallel or in combination [37–39,42,44]. Similarly, there are various types of clustering techniques [45] for creating nodes.

### 2.4.1. The mathematical “lenses” function adopted in this work

The outcome of TDA is largely influenced by the choice of function(s) used to partition the dataset. Any function that maps a data point to a numerical value can serve as a “lens”, offering flexibility in selecting mathematical function families. Some of these families are better suited than others to provide a thorough understanding of the dataset [38,39, 41,42]. Without being exhaustive, we can mention “lenses” derived from statistics (e.g., average, max, min, etc.), chemometrics (e.g., scores from principal component analysis, support vector machine distance from hyperplane, etc.), or geometry (e.g., centrality, curvature, etc.). In this work, two “lenses” were selected for the construction of the topological network. One of them refers to the Gaussian density function of the metric. Assuming a collection of N points as a point cloud data denoted as $\mathbb{Z}$, and introducing $d(x,y)$ the distance between $x, y \in \mathbb{Z}$, the Gaussian density function corresponds here to a row-wise Gaussian kernel estimator over the data according to:

$$f(x) = \sum_{y \in \mathbb{Z}} e^{-d^2(x,y)} \quad (1)$$
The second “lens” we used in this work is the nanoindentation value ($\delta^*$) which marks the transition between the non-linear elastic deformation of the cell wall after indentation by the AFM tip, and the linear compliance regime in the AFM force curves. The former lens allows the identification of changes in the occurrence of effects of TiO₂NPs on E. Coli cells with changing TiO₂NPs concentration, while the latter lens specifies the extent of cell surface alterations, recalling that changes in $\delta^*$ are associated, for example, with NPs-induced removal of LPS and depend on the cell wall compartment (outer/inner membrane, or peptidoglycan layer) affected by TiO₂NPs [8].

### 3. Results and discussion

The TDA was applied according to two different strategies defined in the caption of Fig. S2. These strategies differ in the amount of data subjected to analysis, the choice of which may depend on the computational resources available.

#### 3.1. Strategy #1: analysis at the single cell level (per exposure condition)

This approach allows the assessment of TiO₂NPs toxicity effects by considering AFM data collected on JW3606 and JW3596 E. coli mutants at the single cell level analysis (i.e., one individual cell per exposure condition and per mutant). The corresponding ensemble of analysed AFM data is $\{\cup_{i,j} \{(E, k_{cell})\}_{i,j,k=1}^{|i|} | i \equiv \text{JW3606}, \text{JW3596} \text{ and } j \equiv \text{NP0}, \text{NP1}, \dots, \text{NP20}\}$ where $k=1$ specifies that one cell per TiO₂NPs concentration is considered. This ensemble represents a total of 120,012 (E, $k_{cell}$) couples. Figs. 3a and 4a show the topological networks generated from two TDA analyses of 120,012 (E, $k_{cell}$) pairs using Gaussian density and nanoindentation $\delta^*$, respectively, as the mathematical lens. The (E, $k_{cell}$) and $\delta^*$ data sets adopted here correspond to the nanomechanical proxies of a selected JW3606 cell and a JW3596 cell (data mixed together) under all TiO₂NPs concentration conditions tested (NP0 to NP20).

Four probability “arms” can be distinguished in the network of Fig. 3a: two maxima, labelled #1 and #2, and two minima labelled #3 and #4, associated with the highest and lowest Gaussian densities, respectively. For a given node of the network, the higher the Gaussian density is, the lower the dispersion of the ensemble of (E, $k_{cell}$) pairs determined over the probed cell surface areas under the examined conditions. Fig. 4a shows a linear-like gradient of the “lens” $\delta^*$ across the whole network whose largest nodes correspond to relatively small $\delta^*$ (ca. 20–40 nm) and smallest ones to larger $\delta^*$ (80–120 nm), the size of the nodes in the network being connected to the number of (E, $k_{cell}$) pairs encountered at given lens value. Figs. 3b and 4b specify the respective contribution of (E, $k_{cell}$) pairs collected at a given TiO₂NPs concentration from NP0 to NP20 on either JW3606 or JW3596 considered separately or jointly. The associated colour scale refers to the number of (E, $k_{cell}$) pairs associated to a given NPj condition (with $j = 0,1,2,5,10$ and 20) with respect to the ensemble of (E, $k_{cell}$) pairs collected over the full range of TiO₂NPs concentrations for the mutants considered either separately or jointly.

We provide below a cross-interpretation of Fig. 3a,b and Fig. 4a,b to demonstrate their capability for identifying TiO₂NPs toxicity action modes on JW3606 and JW3596 cells. First, the (E, $k_{cell}$) pairs at NP0 for JW3606 (Fig. 3b) are mainly located in the “arms” #2, #3 and #4 shown in Fig. 3a, with 20 % of the total amount of (E, $k_{cell}$) data distributed in these parts of the network. This finding reflects a significant heterogeneity in the spatial distribution of the E and $k_{cell}$ surface features of JW3606, which is related to the heterogeneity in the distribution of biomolecules such as LPS carried by the cell surface. This heterogeneity is confirmed by TDA at NP0 for JW3596, with most of the NP0-(E, $k_{cell}$) pairs now found in arms #3 (ca. 35 %) and #2 (ca. 20 %). This is consistent with a more homogeneous JW3596 cell surface (with truncated LPS) as compared to JW3606, which has longer LPS surface structures [8,17]. Fig. 4a and b further demonstrate slightly higher

maximum values reached by $\delta^*$ for JW3596 compared to JW3606 within the regions of the TDA network corresponding to the highest contribution (percentage) of (E, $k_{cell}$) pairs from NP0 contribution to the whole network. For JW3596, the associated enlightened parts of the network further distributed over larger regions, which is characteristic of broader distribution of $\delta^*$ values. This finding agrees with an increased weakening of the cell surface envelope following truncation of their LPS inner core, resulting in somewhat softer JW3596 cell surfaces, a conclusion that holds at least for the bacterium individual selected for the analysis. With increasing TiO₂NPs concentration, remarkable distinct changes in the topological networks are observed for both mutants. For JW3606, NP1-(E, $k_{cell}$) data are mainly found in arm #4 (ca. 35 %) and #2 (ca. 5 %) of the network constructed with the Gaussian density lens, whereas for JW3596 they are distributed in arms #1 (ca. 35 %) and #3 (ca. 60 %). This clearly reflects the differential response of the two selected mutants to TiO₂NPs exposure. While for JW3606 the network regions of highest Gaussian density are shifted downwards from NP0 to NP1, for JW3596, this shift operates in the opposite direction. Fig. 4a and b specify that these shifts evidenced for JW3606 and JW3596 feature a decrease and an increase in $\delta^*$, respectively, i.e., a rigidification and a softening of the cell envelop upon TiO₂NPs action under NP1 condition.

The rigidification of the cell surface results from TiO₂NPs-induced abrasion of the protruding soft LPS, whereas the softening correlates with TiO₂NPs-mediated degradation of the supporting cell outer membrane, which was weakened by LPS truncation prior to nanoparticle exposure. With the switch from NP1 to NP2 conditions, essentially all (E, $k_{cell}$) data for JW3606 are located exclusively in arm #4 defined by lowest Gaussian density lens values (Fig. 3a and b), and this change is accompanied by a significant decrease in $\delta^*$ (from ca. 60 nm for NP1 to ca. 20 nm for NP2, Fig. 4). Stated differently, the TiO₂NPs-induced rigidification of the cell surface from NP0 to NP1 previously invoked is intensified with increasing TiO₂NPs concentration from NP1 to NP2. In contrast, the cell wall status of JW3596 under NP2 condition is very similar to that commented for NP0 condition (Figs. 2 and 3), marking a kind of adaptation of JW3596 to TiO₂NPs-induced stress. These elements correlate with a higher amount of membrane vesicles secreted by JW3596 (even in the absence of NPs): these vesicles indeed act as agents that mitigate the adverse effects of TiO₂NPs via their role as electrostatic bait for TiO₂NPs and their evacuation of potentially harmful membrane products generated by TiO₂NPs action [17]. Upon further increase in TiO₂NPs concentration from NP2 to NP5 condition, for JW3606 the coloured nodes in Fig. 3b are shifted upwards in the topological network and are mostly in arms #2 and #4 (<10 % and approximately 25 % of the data, respectively), similar to the situation observed at NP1. This correspondence between the cell surface status under NP1 and NP5 conditions is also reflected in the topological networks shown in Fig. 4a and b. From a biophysical point of view, this finding indicates that the JW3606 cell barrier structure is now somewhat less resistant to TiO₂NPs action under NP5 condition compared to the NP2 case (higher indentation $\delta^*$): the rigidification process operational from NP0 to NP2 has thus been replaced by a softening of the cell surface under NP5 measuring condition. This transition results from a TiO₂NPs-caused degradation of the originally rigid JW3606 outer cell membrane following significant abrasion of the softer LPS protective layer operated at lower TiO₂NPs concentrations. With respect to JW3596, the nodes of the topological network relative to the NP5-related (E, $k_{cell}$) data are now located in arms #3 and #1 (ca. 100 % and 65 %, respectively, Fig. 3b) and correspond to increased values of $\delta^*$ compared to the NP2 condition (ca. 70 nm to ca. 120 nm, Fig. 4b), reflecting an increased softening of the cell wall caused by TiO₂NPs. Finally, with increasing TiO₂NPs concentration from NP5 to NP10 and NP20 conditions, most of the corresponding (E, $k_{cell}$) data are gradually shifted downward in the Gaussian density-based networks of Fig. 3b, i.e., in arm #4 for JW3606 (ca. 35 %) at NP20, and in arms #2 (ca. 15 %) and #4 (ca. 10 %) for JW3596 at NP20. These data regions are associated with a progressive decrease of the AFM tip indentation for both mutant cells (Fig. 4b), more
so for JW3606. The results suggest that the AFM tip probe a rigid cell wall component, identified by Pagnout et al. [8] as the peptidoglycan layer, and the latter increasingly exposed after the significant alteration of the outer cell membrane at TiO₂NP concentrations below 5 mg/L. The extend of heterogeneity in the distributed values of δ* is clearly reduced for JW3606 mutant from NP5 to NP20, while it increases for JW3596. The responses of cells across the NP5 to NP20 gradient in TiO₂NPs concentration are indicative of major impacts on the cell wall structure at such high level of nanoparticles content in the extracellular medium.

As an intermediate conclusion, the topological networks obtained following strategy #1 make it possible to identify the existence of clearly differentiated responses of JW3606 and JW3596 to TiO₂NPs exposure (compare left and right columns with the middle column in Fig. 3b, 4b), and highlight whether TiO₂NPs lead to rigidification or softening of the cell envelope depending on the cell surface phenotype and TiO₂NPs concentration. Regardless of the “lens” chosen for topological network construction, the specificity of the differentiated response of each mutant cell to TiO₂NPs exposure can also be understood at a glance from the topological networks developed from the TDA of the (E, kcell) data pertaining to each mutant cell and compiled over the full range of TiO₂NPs concentrations examined (Figs. 3c and 4c).

## 3.2. Strategy #2: multi-individual cell level analysis (8 cells)

These second approach addressed TiO₂NP toxicity effects by considering AFM data collected on JW3606 or JW3596 E. coli mutants at a multi-individual level (8 cells per condition for a given selected mutant). The corresponding ensemble of analysed AFM data is therefore

{∪ᵢⱼ ({E, kcell})ᵢⱼₖ | i ≡ JW3606 or JW3596 and j ≡ NP0, NP1, ..., NP20}, which represents a total of 120,012 (E, kcell) couples. Figs. 5 and 6 show the topological networks constructed from the TDA of 120,000 (E, kcell) pairs measured on 8 cells of mutant JW3606 or JW3596, respectively, using the Gaussian density and the indentation δ* as “lens”, respectively. The ensemble of analysed data refers to the whole set of NPj conditions tested (panels a,b in Figs. 5 and 6) or to the NPj condition considered separately (panels c,d in Figs. 5 and 6). Thus, the focus here is on the cell response to TiO₂NPs examined at the multi-individual level for a given cell surface phenotype. Fig. 5a shows three main probability “arms” for JW3606, a maximum (#1) and two minima (#2, #3), and similar features apply to JW3596 (Fig. 6a). The NP0-related data for JW3606 are mainly located in the maximum arm #1, which represents 35 % of the corresponding (E, kcell) data. This topological fingerprint of the hereafter denoted NP0 mode is associated with indentation values covering a range from 35 nm to 125 nm (Fig. 5b), which is clearly wider than the range identified in Fig. 3b for a single JW3606 cell. This is a direct consequence of the surface heterogeneity that necessarily differs from one JW3606 cell to another. In contrast, the 8 selected JW3596 cells basically display a homogeneous distribution of (E, kcell) pairs over the entire topological network (Fig. 6a-c) under NP0 condition, thus spreading over the entire window of Gaussian density values. Despite of such a “smeared-out” topological NP0-mode for JW3596, the indentation values are spread over the narrow window of 40 nm-80 nm (Fig. 6b-d), which is consistent with the shorter LPS of JW3596. With increasing TiO₂NPs concentration from NP0 to NP1, the (E, kcell) pairs for JW3606 slightly move from arm #1 to arm #3 of the topological network and the indentation decreases (Fig. 5), which conforms to the

<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 3.** Topological data analysis according to strategy #1 (Fig. S2b, ●) applied to the ensemble of data defined by {∪ᵢⱼ ({E, kcell})ᵢⱼₖ=₁ | i ≡ JW3606, JW3596 and j ≡ NP0, NP1, ..., NP20} using the Gaussian density “lens”. **a.** The topological network, collecting the nanomechanical properties of both JW3606 and JW3596 over the whole range of TiO₂NPs concentrations tested, was generated with an interval length of 1.62 and a 50 % overlap between consecutive intervals in order to partition the Gaussian density “lens” values ranging from 1.00 to 88.18. **b.** Generation of daughter networks as detailed in Fig. S2b, ●, which quantifies the percentage of (E, kcell) couples originating from either JW3606 (left column) or JW3596 (right column), or both (middle column) for each TiO₂NPs concentration tested. **c.** Generation of daughter networks as shown in Fig. S2b, ●, distinguishing the respective contributions of JW3606 and JW3596 to the network shown in panel (a).</figcaption></figure>
behaviour observed at the single cell level (Figs. 3 and 4).

By further increasing the TiO₂NPs concentration to NP2, most of the corresponding (E, kcell) pairs are now located at the extremity of arm #3, implying that all probed cells have responded in a similar manner to TiO₂NPs exposure. Under NP5, NP10 and NP20 conditions, the modes of action of TiO₂NPs on JW3606 result in well-identified patterns of nodes located along arm #3, in arm #2 and at the edge of arm #3, respectively. This behaviour is associated with increasing indentation values from NP5 to NP10, while NP20 exposure leads to a dramatic decrease in indentation. While the latter decrease is qualitatively consistent with the one identified for a single cell (Figs. 3 and 4), the change in the inden- tation from NP5 to NP10 at the multi-individual level is opposite to that revealed from the analysis of the nanomechanical data at the scale of a single cell. Upon transitioning from NP0 to NP1 and NP2 exposure conditions, the (E, kcell) pairs belonging to the analysed JW3596 cells are first positioned in the central part of the topological network and then migrate towards the arms #1 and #2, while the corresponding inden- tation values gradually increase to reach extremes located at the top nodes of the δ*-based topological network (Fig. 6c and d). This is qualitatively in agreement with the trend discussed at the single cell level. Quantitatively, the transition from intermediate to extreme indentation values occurs at lower TiO₂NPs concentrations compared to that revealed at the multi-individual scale. The topological network under NP5 conditions shares common properties with that generated in the absence of TiO₂NPs. Clearly, the NP5 exposure condition marks a transition towards TiO₂NPs action modes that are at higher concentra- tions (NP10 and NP20) where (E, kcell) couples are gradually shifted towards the extremity of “arm” #3. JW3596 cells exhibit the lowest

indentation values at such high TiO₂NPs doses. The comparison between Figs. 6c and 4b shows that the impact of TiO₂NPs under NP10 and NP20 conditions is more pronounced at the multi-individual scale as compared to single cell level.

4. Conclusion

Our topology-based analysis of nanomechanical cell surface prop-
erties collected by nm-resolved force spectroscopy allows a rapid visu-
alization of the different modes of action of TiO₂NPs on E. coli cells as a
function of nanoparticle exposure concentration and cell surface
phenotype. Depending on the ensemble of data subjected to TDA, the
reported method can probe the cell response to TiO₂NPs at different
biological scales, from the single cell to a collection of multi-individuals.
The results highlight the existence of distinct cell resistance/sensitivity
patterns depending on the composition of cell surface lipopolysaccha-
rides (LPS). The reading of the corresponding topological networks is
facilitated by the distinct nature of the “lenses” adopted for their gen-
eration, namely: a statistical-mathematical “lens” that underscores the
multiscale heterogeneity of cell response, and a physically meaningful
“lens” that reflects the way in which TiO₂NPs lead to rigidification or
softening of the cell envelope. In contrast to previous studies, the pro-
posed TDA method is not biased by any a priori choice of NP toxicity
descriptors, and is based on relevant NPs-induced damage to the cell
envelope barrier, which is the very first target of the nanoparticulate
stressors. Accordingly, the TDA-AFM combination provides a new and
powerful tool for early diagnosis of nanoparticle toxicity to microor-
ganisms, thus offering an alternative to standardized ecotoxicological

<figure><img src="image_8.png" /></figure>

<figure><img src="image_9.png" /><figcaption>**Fig. 4.** Topological data analysis according to strategy #1 (Fig. S2b, ●) applied to the ensemble of data defined by {∪<sub>i,j</sub>{(E, k<sub>cell</sub>)<sub>i,j,k=1</sub> | i ≠ JW3606, JW3596 and j ≠ NP0, NP1, ..., NP20} using the indentation δ* “lens”. a, The topological network, collecting the nanomechanical properties of both JW3606 and JW3596 over the whole range of TiO<sub>2</sub>NPs concentrations tested, was generated with an interval length of 1.62 and a 50 % overlap between consecutive intervals in order to partition the indentation “lens” values ranging from 15 nm to 120 nm b, Generation of daughter networks as shown in Fig. S2b, ●, which quantifies the percentage of (E, k<sub>cell</sub>) couples originating from either JW3606 (left column) or JW3596 (right column), or both (middle column) for each TiO<sub>2</sub>NPs concentration tested. c, Generation of daughter networks as detailed in Fig. S2b, ●, distinguishing the respective contributions of JW3606 and JW3596 to the network shown in panel (a).</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>**Fig. 5.** Topological data analysis according to strategy #2 (Fig. S2c, ●) applied to the ensemble of data defined by {$\cup_{j,k}\{(E, k_{cell})\}_{i,j,k} | i \equiv \text{JW3606}; j \equiv \text{NP0, NP1, \dots, NP20 and } k = 1, \dots, 8$} using the Gaussian density “lens” and the indentation $\delta^*“lens$. **a.** The topological network, collecting nanomechanical properties of JW3606 over the whole range of TiO₂NPs concentration, was generated with an interval length of 1.73 and a 50 % overlap between consecutive intervals in order to partition the Gaussian density “lens” values ranging from 1 to 70.14. **b.** The topological network, collecting nanomechanical properties of JW3606 over the entire range of TiO₂NPs concentration, was generated with an interval length of 2.26 and a 50 % overlap between successive intervals in order to partition the indentation “lens” values ranging from 13.52 to 169.58. **c.** and **d.** Generation of daughter networks as shown in Fig. S2c, ⊕, which quantifies the percentage of (E, $k_{cell}$) couples originating from JW3606 for each TiO₂NPs concentration tested.</figcaption></figure>

tests based on macroscopic toxicity endpoints with limited mechanistic value. A promising follow-up of the proposed methodology is the topological analysis of AFM-derived cell nanomechanics, complemented by cell surface vibrational spectroscopy data, therewith exploiting the full benefits of combined AFM-Raman or AFM-IR techniques.

### CRediT authorship contribution statement

**Marc Offroy:** Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.
**Ludovic Duponchel:** Writing – review & editing, Validation, Investigation, Formal analysis.
**Angelina Razafitianamaharavo:** Writing – review & editing, Validation, Resources, Methodology, Formal analysis, Data curation.
**Christophe Pagnout:** Writing –

review & editing, Validation, Resources, Investigation.
**Jérôme F.L. Duval:** Writing – review & editing, Visualization, Validation, Supervision, Methodology, Investigation, Funding acquisition, Conceptualization.

### Code availability

The homemade MATLAB codes for the evaluation of cell surface nanomechanics from Atomic Force Microscopy (AFM) data and for Topological Data Analysis (TDA) are available upon request.

### Funding sources

M.O.*†, J.F.L.D.** and C.P.** acknowledge funding of this work (*) by the Lorraine Earth and Environment Observatory (OTELo) through
a. Network generation for JW3596 with gaussian density 'lens'

<figure><img src="image_11.png" /></figure>

b. Network generation for JW3596 with indentation $\delta^*$ 'lens'

<figure><img src="image_12.png" /></figure>

c. Percentage of (E, $k_{cell}$) pairs for a given NPs concentration

<figure><img src="image_13.png" /></figure>

NP1

<figure><img src="image_14.png" /></figure>

NP5

<figure><img src="image_15.png" /></figure>

NP20

<figure><img src="image_16.png" /></figure>

d. Percentage of (E, $k_{cell}$) pairs for a given NPs concentration

<figure><img src="image_17.png" /></figure>

NP2

<figure><img src="image_18.png" /></figure>

NP1

<figure><img src="image_19.png" /></figure>

NP5

NP20

<figure><img src="image_20.png" /><figcaption>**Fig. 6.** Topological data analysis according to strategy #2 (Fig. S2c, ●) applied to the ensemble of data defined by $\{\cup_{i,j,k}((E, k_{cell})_{i,j,k} | i \equiv JW3596; j \equiv NP0, NP1, \dots, NP20 \text{ and } k = 1, \dots, 8)\}$ using the Gaussian density “lens” and the indentation $\delta^*$ “lens”. **a.** The topological network, collecting nanomechanical properties of JW3606 over the whole range of TiO₂NPs concentration, was generated with an interval length of 2.72 and a 50 % overlap between consecutive intervals in order to partition the Gaussian density “lens” values ranging from 1 to 109.92. **b.** The topological network, collecting nanomechanical properties of JW3606 over the whole range of TiO₂NPs concentration, was generated with an interval length of 2.70 and a 50 % overlap between consecutive intervals in order to partition the indentation “lens” values ranging from 10.59 to 156.78. **c.** and **d.** generation of daughter networks as detailed in Fig. S2c, ●, which quantifies the percentage of (E, $k_{cell}$) couples originating from JW3596 for each TiO₂NPs concentration tested.</figcaption></figure>

the **TOPOTOX** project and (**) by former Fondation Rovaltain (now Fondation evertéa), https://fcsrovaltain.org/, France through **EVA-MINTOX** project. (†) This work is also partly funded by Carnot ICEEL (Grand Est) via **TRANSFUSION** project.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.talanta.2024.127482.

## Data availability

Data used in this article will be available upon request to corresponding author.

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