This study was carried out with the bacterial strain Stenotrophonas maltophilia 114N-Sm provided by UNIR association (http://www.unir.org). The strain was stored at −20 °C, transferred twice in TSB (Trypcase Soy Broth, BioMérieux) before being cultivated overnight in 100 ml of TSB in continuous flow slide culture at 30 °C under oxygenated conditions.

Bacterial cells in stationary phase were washed by a succession of three centrifugations ($7000g$, 4 °C, 10 min) and resuspensions in 150 ml NaCl. Bacterial concentration was adjusted to 10⁹ CFU/ml by measurements of the absorbance ($A_{400\mathrm{nm}}=0.8$). Two millilitres of the suspension were poured into a flow cell (BST FC81, Biosurface Technology, Bozeman, USA) with a sterile syringe. In this experimental setup, the biofilms grow up on the glass cover slit of the flow cell ($0.17\times 24\times 60\text{mm}$). After 3 h of static adhesion in NaCl 150 mM, a bulk laminar flow rate of 0.5 ml min⁻¹ of growth medium (TSB 1:10) crosses the flow cell in order to eliminate planktonic cells, to allow adherent bacteria to multiply and to form a biofilm (flow obtained from a Watson and Marlow 205S peristaltic pump). The biofilm development period in dynamic conditions prior to FCS experiments was always 24 h at 20 °C in order to minimize bacterial physiological variations in the biofilm structure and thus artefacts in the FCS measurements. Stenotrophonas maltophilia biofilms (Fig. 1) have been extensively studied and represent well-defined systems with mushroom-like structure (zone 2) of ∼30-μm thickness separated by homogeneous layers of bacteria (zone 1) of less than 10 μm. Biofilm depth was determined manually using the computer-controlled focusmeter of a SCLM system (TCS SP2, Leica Microsystems, France) and defined with respect to the cover slit surface (i.e. at the attachment of the biofilm); the top layer of the biofilm (∼30 μm from the glass cover slit) corresponds to the interface with the flowing growth medium.

The model viral of particle used in this study was a C2 bacteriophage infecting Lactococcus lactis subsp. lactis. The 22163-bp genome of this lactococal phage was fully sequenced [12]. The C2 phage exhibits a prolate structure with a 100-nm head and a 200-nm non-contractile tail. Lactococcus lactis was cultivated when necessary in M17 growth medium (Oxoid, France) supplemented with 0.5% of glucose and incubated at 30 °C overnight. Phage C2 and the C2-sensitive strain Lactococcus lactis, subsp. lactis were provided by S. Kulakauskas (INRA URLGA, Jouy-en Josas).

Phage titration was performed using the serial dilution technique and the formation of lytic plaques on a layer of the sensitive bacteria on a Petri dish, as described previously [13]. Experimentally, 0.1 ml of the phage suspension was added to 0.2 ml of a mid-log-phase bacterial culture of the C2-sensitive bacteria L. lactis. 30 μl of CaCl₂ 1 M were added to favour phage infection, and the mixture was incubated 10 min at 30 °C. Each mixture was added to 3 ml of soft agar (M17 Oxoid supplemented with 8 g l⁻¹ of agar and 0.5% of glucose) in order to create a soft double layer on agar plates (M17 Oxoid supplemented with 15 g l⁻¹ of agar and 0.5% of glucose). Petri dishes were incubated overnight at 30 °C in order to enumerate the visible lytic plaques.

For phage amplification, 10⁸ PFU (Plaque Forming Units) of phage C2 were added to 400 ml of a L. lactis culture (DO_{600 nm} = 0.1). Infected bacterial cells were incubated at 30 °C until clearance of the suspension. The mixture was then centrifuged to eliminate bacterial debris for 10 min at $7000g$ and 4 °C. Phage particles were then washed in NaCl 150 mM by a centrifugation at $18000g$ for 6 h. The pellet was resuspended in 10 ml of 150 mM NaCl and sterilized by filtration (0.22 μm, Steriflip, Millipore). The final phage suspension titrated 10¹⁰ PFU/ml was stored at 4 °C.

The anionic carboxylate-modified fluorescent latex beads of 110-nm diameter (range size of bacteriophage head), obtained from Molecular Probes were used as reference. The beads were used in suspension in deionised water (Purit, France). The solutions were filtered and sonicated before each experiment in order to eliminate most of the aggregates and to obtain a final concentration from 1 nM (in solution) to 10 nM (in biofilms). The latex beads could be considered to have a globular structure, enabling an estimation of their diffusion coefficient using the Stokes equation.

The selection criteria for bacteriophage fluorescent labelling were imposed by the experimental conditions required for FCS under TPE: (i) the fluorophore must be excited by two photons in the wavelength range 700–900 nm; (ii) detection of the fluorescence signal emitted during the counting interval needed to be significant despite the low excitation energy and the low fluorophore concentration used, which required to use a fluorophore with a significant fluorescence quantum yield; (iii) the fluorophore must be able to label the bacteriophage and not the living cells inside the biofilms. Because of these constraints, the fluorescent probe used to label the C2 bacteriophage was Sytox green (Molecular probes). The maximal concentration of labelled bacteriophages was obtained by adding 30 μl of Sytox green (5 mM solution) to 5 ml of C2 bacteriophage suspension titrated at 10¹⁰ PFU ml⁻¹. The excess of free Sytox green was removed by careful rinsing. The labelled bacteriophage solution was used as it was for FCS measurements in biofilms and diluted by a factor 10 for experiments in solution. Before the FCS measurements inside biofilms, the growth medium flow was stopped and 2 ml of fluorophores were injected aseptically through the flow cell.

The TPE experimental system used in this study has been described in detail elsewhere [14]. Briefly, the fluorescence excitation source was a femtosecond Ti:Sapphire laser (MIRA 900, Coherent Inc., Santa Clara, CA) pumped in the green by a continuous-wave diode-pumped solid-state laser (VERDI, Coherent Inc.) generating 100-fs pulses at a 76-MHz repetition rate with about 700-mW average power output. An excitation wavelength of 890 nm was fixed for all of the TPE experiments described here. The laser beam is expanded 3 times at the entrance of the microscope in order to reach a diameter of approximately 5 mm in diameter to fill the back aperture of the objective. After the beam expander, parallel laser light epi-illuminates a Zeiss $63\times 1.4$ numerical aperture, oil immersion objective. Fluorescence emission was collected through the same objective, separated from the excitation radiation by a dichroic mirror. It was then filtered through short-pass filters to absorb any possible diffused infrared excitation light and focused on the surface of a photomultiplier tube (R7205-01, Hamamatsu, Massy, France). This device was connected to a discriminator (TC 454, Oxford Instruments Inc., Oxford, UK), and the output signal was transmitted to a digital autocorrelator module (Flex2kx2-12, correlator) that computes on-line the correlation function of the fluorescence fluctuations. To measure translational diffusion time with 10 to 20% (see below) accuracy, data recording times are 60–100 s for solution acquisitions and 100–300 s in the biofilms and corresponds to 10–20 iterations, respectively. The data are stored in the computer and analysed by a home-written routine that allows to: (i) select and average chosen successive acquisitions, (ii) make anomal diffusion fit if necessary (see below), (iii) calculate the associated standard deviations.

A general concern in fluorescence microscopy measurements and especially for applications with slow moving particles through biofilm depth is the risk of photobleaching the fluorophores at high laser power values. For this reason, we always used less than 1 mW at the sample and thus no cellular degradation was observed during the time of experiments as verified by confocal microscopy with the live/dead bacterial viability kit (Molecular probes). Furthermore, while IR excitation wavelength was used (890 nm), no significant temperature increase due to water absorption was observed.

The conceptual and theoretical basis of FCS has been well established [7,9,15,16]. Assuming that the excitation intensity profile could be approximated using a three-dimensional Gaussian distribution, the fluorescence correlation curves in the case of free Brownian motion of molecules can be fitted using the following normalized autocorrelation function:

Under biphotonic excitation, the translational diffusion time can be related to the beam waist ${\omega }_0$ and the diffusion coefficient $D_{\mathrm{t}}$ of the fluorophore by the relation:

For approximately spherical particles (such as latex beads) of hydrodynamic radius (R), the local viscosity η of the medium can be obtained via the Stokes–Einstein equation:

In the presence of obstacles that lead to deviation of the molecules from Brownian motion (called anomal diffusion) [7], the normalized autocorrelation function is transformed into:

The parameter $d_{\mathrm{w}}$ is equal to 2 for free diffusion and increases with increasing obstacle concentration. This results in an increase of the translational diffusion time, ${\tau }_{\mathrm{D}}$, and to a decrease of the apparent diffusion coefficient, $D_{\mathrm{t}}$.

Typical experimental fluorescence correlation curves obtained in aqueous solutions at room temperature (water viscosity ${\eta }_{\mathrm{w}}=0.96\text{cP}$ at 295 K) for latex beads and free fluorescent labelled bacteriophages are shown in Fig. 2. The ${\tau }_{\mathrm{D}}$ and N values are obtained by fitting the experimental curves considering Brownian motion diffusion (Eq. (1)). The corresponding diffusion coefficients (D) calculated using Eq. (2) were 3.1 μm² s⁻¹ and 1.2 μm² s⁻¹ for the carboxylate beads and the viral particles, respectively. It can be observed that this D value is ∼2.6 time lower for the bacteriophage compared to fluorescent beads revealing that the exocellular tail of the viral particle significantly reduces its mobility.

Moreover, the experimental diffusion coefficient measured for the fluorescent microspheres is in good agreement with the theoretical value ($D_0$) expected from the Stokes–Einstein equation ($D_0=4.0\text{μ}{\text{m}}^2{\text{s}}^{\mathrm{-1}}$), a result that demonstrates the accuracy of our FCS technique.

We have observed that, in our experimental conditions, the bacterial autofluorescence as well as the overall biofilm movement were able to create a correlation signal (Fig. 3, inset). However, the translational diffusion coefficient associated to this background movement (${\tau }_{\mathrm{D}}>50\text{s}$) was out of range compared to the ${\tau }_{\mathrm{D}}$ values obtained for the fluorescent probes (${\tau }_{\mathrm{D}}<150\text{ms}$) and thus did not interfere with the fluorophore diffusion.

3.2.1 Latex beads

3.2.2 Fluorescent labelled bacteriophages

Fluorescent correlation curve profiles obtained for the labelled bacteriophages were markedly dependent upon local biofilm structure. Within more homogeneous structure (zone 1), the fluorescence correlation curves were already distorted in comparison with that obtained for free bacteriophages. These distortions increased with the compactness of local biofilm structure. Fig. 4 provides a series of fluorescent correlation curves at different depths within a mushroom-like region (zone 2) of the biofilm, nonetheless revealing any significant difference in all the bulk of the mushroom structure.