Atomic force microscopy (AFM) has now become a powerful technique for investigating on a molecular level, surface forces, nanomechanical properties of deformable particles, biomolecular interactions, ...kinetics, and dynamic processes. This paper specifically focuses on the analysis of AFM force curves collected on biological systems, in particular, bacteria. The goal is to provide fully automated tools to achieve theoretical interpretation of force curves on the basis of adequate, available physical models. In this respect, we propose two algorithms, one for the processing of approach force curves and another for the quantitative analysis of retraction force curves. In the former, electrostatic interactions prior to contact between AFM probe and bacterium are accounted for and mechanical interactions operating after contact are described in terms of Hertz-Hooke formalism. Retraction force curves are analyzed on the basis of the Freely Jointed Chain model. For both algorithms, the quantitative reconstruction of force curves is based on the robust detection of critical points (jumps, changes of slope or changes of curvature) which mark the transitions between the various relevant interactions taking place between the AFM tip and the studied sample during approach and retraction. Once the key regions of separation distance and indentation are detected, the physical parameters describing the relevant interactions operating in these regions are extracted making use of regression procedure for fitting experiments to theory. The flexibility, accuracy and strength of the algorithms are illustrated with the processing of two force-volume images, which collect a large set of approach and retraction curves measured on a single biological surface. For each force-volume image, several maps are generated, representing the spatial distribution of the searched physical parameters as estimated for each pixel of the force-volume image.
In this work, we report original analytical expressions defining the electrophoretic mobility of composite soft particles comprising an inner core and a surrounding polymer shell with differentiated ...permeabilities to ions from aqueous background electrolyte and to fluid flow developed under applied DC field conditions. The existence of dielectric permittivity gradients operational at the core/shell and shell/solution interfaces is accounted for within the Debye–Hückel approximation and flat plate configuration valid in the thin double layer regime. The proposed electrophoretic mobility expressions, applicable to weakly to moderately charged particles with size well exceeding the Debye layer thickness, involve the relevant parameters describing the particle core/shell structure and the electrohydrodynamic features of the core and shell particle components. It is shown that the analytical expressions reported so far in literature for the mobility of hard (impermeable) or porous particles correspond to asymptotic limits of the more generic results detailed here. The impacts of dielectric‐mediated effects of ions partitioning between bulk solution and particle body on the electrophoretic response are further discussed. The obtained expressions pave the way for a refined quantitative, analytical interpretation of electrophoretic mobility data collected on soft (nano)particles (e.g., functionalized dendrimers and multilayered polyelectrolytic particles) or biological cells (e.g., viruses) for which the classical hard core‐soft shell representation is not appropriate.
The physicochemical properties and dynamics of bacterial envelope, play a major role in bacterial activity. In this study, the morphological, nanomechanical and electrohydrodynamic properties of ...Escherichia coli K-12 mutant cells were thoroughly investigated as a function of bulk medium ionic strength using atomic force microscopy (AFM) and electrokinetics (electrophoresis). Bacteria were differing according to genetic alterations controlling the production of different surface appendages (short and rigid Ag43 adhesins, longer and more flexible type 1 fimbriae and F pilus). From the analysis of the spatially resolved force curves, it is shown that cells elasticity and turgor pressure are not only depending on bulk salt concentration but also on the presence/absence and nature of surface appendage. In 1 mM KNO(3), cells without appendages or cells surrounded by Ag43 exhibit large Young moduli and turgor pressures (∼700-900 kPa and ∼100-300 kPa respectively). Under similar ionic strength condition, a dramatic ∼50% to ∼70% decrease of these nanomechanical parameters was evidenced for cells with appendages. Qualitatively, such dependence of nanomechanical behavior on surface organization remains when increasing medium salt content to 100 mM, even though, quantitatively, differences are marked to a much smaller extent. Additionally, for a given surface appendage, the magnitude of the nanomechanical parameters decreases significantly when increasing bulk salt concentration. This effect is ascribed to a bacterial exoosmotic water loss resulting in a combined contraction of bacterial cytoplasm together with an electrostatically-driven shrinkage of the surface appendages. The former process is demonstrated upon AFM analysis, while the latter, inaccessible upon AFM imaging, is inferred from electrophoretic data interpreted according to advanced soft particle electrokinetic theory. Altogether, AFM and electrokinetic results clearly demonstrate the intimate relationship between structure/flexibility and charge of bacterial envelope and propensity of bacterium and surface appendages to contract under hypertonic conditions.
Latest knowledge on the reactivity of charged nanoparticulate complexants toward aqueous metal ions is discussed in mechanistic detail. We present a rigorous generic description of electrostatic and ...chemical contributions to metal ion binding by nanoparticulate complexants, and their dependence on particle size, particle type (i.e., reactive sites distributed within the particle body or confined to the surface), ionic strength of the aqueous medium, and the nature of the metal ion. For the example case of soft environmental particles such as fulvic and humic acids, practical strategies are delineated for determining intraparticulate metal ion speciation, and for evaluating intrinsic chemical binding affinities and heterogeneity. The results are compared with those obtained by popular codes for equilibrium speciation modeling (namely NICA-Donnan and WHAM). Physicochemical analysis of the discrepancies generated by these codes reveals the a priori hypotheses adopted therein and the inappropriateness of some of their key parameters. The significance of the characteristic time scales governing the formation and dissociation rates of metal–nanoparticle complexes in defining the relaxation properties and the complete equilibration of the metal–nanoparticulate complex dispersion is described. The dynamic features of nanoparticulate complexes are also discussed in the context of predictions of the labilities and bioavailabilities of the metal species.
Atomic Force Microscopy (AFM) is a powerful technique for the measurement of mechanical properties of individual cells in two (
x
×
y
) or three (
x
×
y
× time) dimensions. The instrumental progress ...makes it currently possible to generate a large amount of data in a relatively short time, which is particularly true for AFM operating in so-called PeakForce tapping mode (Bruker corporation). The latter corresponds to an AFM probe that periodically hits the sample surface while the pico-newton level interaction force is recorded from cantilever deflection. The method provides unprecedented high-resolution (a few tens of nm) imaging of the mechanical features of soft biological samples (
e.g.
bacteria, yeasts) and of hard abiotic surfaces (
e.g.
minerals). The rapid conversion of up to several tens of thousands spatially resolved force curves typically collected in AFM PeakForce tapping mode over a given cell surface area into comprehensive nanomechanical information requires the development of robust data analysis methodologies and dedicated numerical tools. In this work, we report an automated algorithm for (i) a rapid and unambiguous detection of the indentation regimes corresponding to non-linear and linear deformations of bacterial surfaces upon compression by the AFM probe, (ii) the subsequent evaluation of the Young modulus and cell surface stiffness, and (iii) the generation of spatial mappings of relevant nanomechanical properties at the single cell level. The procedure involves consistent evaluation of the contact point between the AFM probe and sample biosurface and that of the threshold indentation value marking the transition between non-linear and linear deformation regimes. For comparison purposes, the former regime is here analyzed on the basis of Hertz and Sneddon models corrected or not for effects of finite sample thickness. Analysis of AFM measurements performed on a selected
Escherichia coli
strain is detailed to demonstrate the feasibility, rapidity and robustness of the here-proposed PeakForce data treatment process. The flexibility of the algorithm allows consideration of force curve parameterizations other than that detailed here, which may be desired for investigation of
e.g.
eukaryotes nanomechanics. The performance of the adopted Hertz-based and Sneddon-based contact mechanics formalisms in recovering experimental data and in identifying nanomechanical heterogeneities at the bacterium scale is further thoroughly discussed.
A numerical method is proposed for the modeling of AFM PeakForce curves and the automated extraction of relevant spatially-resolved nanomechanical properties of turgescent cells.
The main driver of the potential toxicity of micro- and nanoplastics toward biota is often the release of compounds initially present in the plastic, i.e., polymer additives, as well as ...environmentally acquired metals and/or organic contaminants. Plastic particles degrade in the environment via various mechanisms and at different rates depending on the particle size/geometry, polymer type, and the prevailing physical and chemical conditions. The rate and extent of polymer degradation have obvious consequences for the uptake/release kinetics and, thus, the bioavailability of compounds associated with plastic particles. Herein, we develop a theoretical framework to describe the uptake and release kinetics of metal ions and organic compounds by plastic particles and apply it to the analysis of experimental data for pristine and aged micro- and nanoplastics. In particular, we elucidate the contribution of transient processes to the overall kinetics of plastic reactivity toward aquatic contaminants and demonstrate the paramount importance of intraparticulate contaminant diffusion.
Potentiometric acid–base titration curves collected on humic (nano)particles as a function of pH and salt concentration reflect the electrostatics of the particles and the amount of chemical charges ...(Q) they carry. In turn, the interpretation of titration data helps quantify their reactivity toward metals provided that both intrinsic chemical and nonspecific electrostatic contributions to proton binding are correctly unraveled. Establishing a titration curve requires several steps, i.e., blank subtraction, relative curve positioning with respect to the electrolyte concentration, and absolute curve positioning achieved by the estimation of particle charge Q 0 at low pH. Failure to properly establish each step may lead to the misevaluation of nanoparticle charging behavior. Here, we report (i) a simple procedure to measure and position titration curves for humic substances (HS) versus salt concentration and (ii) an original approach for absolute curve positioning upon the exploitation of proton affinity spectra. The latter do not depend on Q 0 and they thus constrain the titration data analysis using the soft Poisson–Boltzmann-based titration (SPBT) formalism for nanoparticles in the thick electric double-layer regime. We illustrate the benefits of our approach by analyzing titration measurements for a large range of humic nanoparticles and by comparing the outcome with results from the literature.
A theory is presented for the electrophoresis of diffuse soft particles in a steady dc electric field. The particles investigated consist of an uncharged impenetrable core and a charged diffuse ...polyelectrolytic shell, which is to some extent permeable to ions and solvent molecules. The diffuse character of the shell is defined by a gradual distribution of the density of polymer segments in the interspatial region separating the core from the bulk electrolyte solution. The hydrodynamic impact of the polymer chains on the electrophoretic motion of the particle is accounted for by a distribution of Stokes resistance centers. The numerical treatment of the electrostatics includes the possibility of partial dissociation of the hydrodynamically immobile ionogenic groups distributed throughout the shell as well as specific interaction between those sites with ions from the background electrolyte other than charge-determining ions. Electrophoretic mobilities are computed on the basis of an original numerical scheme allowing rigorous evaluation of the governing transport and electrostatic equations derived following the strategy reported by Ohshima, albeit within the restricted context of a discontinuous chain distribution. Attention is particularly paid to the influence of the type of distribution adopted on the electrophoretic mobility of the particle as a function of its size, charge, degree of permeability, and solution composition. The results are systematically compared with those obtained with a discontinuous representation of the interface. The theory constitutes a basis for interpreting electrophoretic mobilities of heterogeneous systems such as environmental or biological colloids or swollen/deswollen microgel particles.
The interfacial structure of natural rubber (NR) colloids is investigated by means of cryogenic transmission electron microscopy (cryo-TEM) and electrokinetics over a broad range of KNO3 electrolyte ...concentrations (4–300 mM) and pH values (1–8). The asymptotic plateau value reached by NR electrophoretic mobility (μ) in the thin double layer limit supports the presence of a soft (ion- and water-permeable) polyelectrolytic type of layer located at the periphery of the NR particles. This property is confirmed by the analysis of the electron density profile obtained from cryo-TEM that evidences a ∼2–4 nm thick corona surrounding the NR polyisoprene core. The dependence of μ on pH and salt concentration is further marked by a dramatic decrease of the point of zero electrophoretic mobility (PZM) from 3.6 to 0.8 with increasing electrolyte concentration in the range 4–300 mM. Using a recent theory for electrohydrodynamics of soft multilayered particles, this “anomalous” dependence of the PZM on electrolyte concentration is shown to be consistent with a radial organization of anionic and cationic groups across the peripheral NR structure. The NR electrokinetic response in the pH range 1–8 is indeed found to be equivalent to that of particles surrounded by a positively charged ∼3.5 nm thick layer (mean dissociation pK ∼ 4.2) supporting a thin and negatively charged outermost layer (0.6 nm in thickness, pK ∼ 0.7). Altogether, the strong dependence of the PZM on electrolyte concentration suggests that the electrostatic properties of the outer peripheral region of the NR shell are mediated by lipidic residues protruding from a shell containing a significant amount of protein-like charges. This proposed NR shell interfacial structure questions previously reported NR representations according to which the shell consists of either a fully mixed lipid–protein layer, or a layer of phospholipids residing exclusively beneath an outer proteic film.
The interactions of bacteria with their environment are governed by a complex interplay between biological and physicochemical phenomena. The main challenge is the joint determination of the ...intertwined interfacial characteristics of bacteria such as mechanical and hydrodynamic softness, interfacial heterogeneity, and electrostatic properties. In this study, we have combined electrokinetics and force spectroscopy to unravel this intricate coupling for two types of Shewanella bacterial strains that vary according to the nature of their outer, permeable, charged gel-like layers. The theoretical interpretation of the bacterial electrokinetic response allows for the estimation of the hydrodynamic permeability, degree of interfacial heterogeneity, and volume charge density for the soft layer that constitutes the outer permeable part of the bacteria. Additionally, the electrostatic interaction forces between an AFM probe and the bacteria were calculated on the basis of their interfacial properties obtained from advanced soft particle electrokinetic analysis. For both bacterial strains, excellent agreement between experimental and theoretical force curves is obtained, which highlights the necessity to account for the interfacial heterogeneity of the bioparticle to interpret AFM and electrokinetic data consistently. From the force profiles, we also derived the relevant mechanical parameters in relation to the turgor pressure within the cell and the nature of the bacterial outer surface layer. These results corroborate the heterogeneous representation of the bacterial interface and show that the decrease in the turgor pressure of the cell with increasing ionic strength is more pronounced for bacteria with a thin surface gel-like layer.
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