Development of an image Mean Square Displacement (iMSD)-based method as a novel approach to study the intracellular trafficking of nanoparticles

Abstract

Fluorescence microscopy and spectroscopy techniques are commonly used to investigate complex and interacting biological systems (e.g. proteins and nanoparticles in living cells), since these techniques can explore intracellular dynamics with high time resolution at the nanoscale. Here we extended one of the Image Correlation Spectroscopy (ICS) methods, i.e. the image Mean Square Displacement, in order to study 2-dimensional diffusive and flow motion in confined systems, whose driving speed is uniformly distributed in a variable angular range. Although these conditions are not deeply investigated in the current literature, they can be commonly found in the intracellular trafficking of nanocarriers, which diffuse in the cytoplasm and/or may move along the cytoskeleton in different directions. The proposed approach could reveal the underlying system's symmetry using methods derived from fluorescence correlation concepts and could recover dynamic and geometric features which are commonly done by single particle analyses. Furthermore, it improves the characterization of low-speed flow motions, when compared to SpatioTemporal Image Correlation Spectroscopy (STICS). Although we present a specific example (lipoplexes in living cells), the emphasis is in the discussion of the method, its basic assumptions and its validation on numeric simulations.

Statement of significance: Recent advances in nanoparticle-based drug and gene delivery systems have pointed out the interactions at cellular and subcellular levels as key-factors for the efficiency of the adopted biomaterials. Such biochemical and biophysical interactions drive and affect the intracellular dynamics, that is commonly characterized by means of fluorescence microscopy and spectroscopy techniques. Here we present a novel Image Correlation Spectroscopy (ICS) method as a promising tool to capture the intracellular behavior of nanoparticles with high resolution and low background's sensitivity. This study overcomes some of the approximations adopted so far, by decoupling the flow terms of the investigated dynamics and thus recovering ensemble's information from specific single particle behaviors. Finally, relevant implications for nanoparticle-based drug delivery are shown.

Keywords: Drug and gene delivery; Image Correlation Spectroscopy (ICS); Intracellular trafficking.

Figure 1

(A, B, C) Sets of 50 tracks and (D, E, F) corresponding average displacements from the origin, for dynamics driven by Brownian diffusion + uniformly distributed flow motion (D = 0.75 10⁻³ μm² s⁻¹; v = 1.5 10⁻² μm s⁻¹; ϕ₀ = π/4 and ψ_A = π/6, ψ_B = π, ψ_C = 3π/2).

Figure 2

(A) $a_{\sigma }^2$ as function of ψ for strongly directed motion and diffusive + flow motion (D = 0.75 10⁻³ μm² s⁻¹; v = 0.5 10⁻² μm s⁻¹). The solid line represents the expected curve obtained from Eq. 15, the dashed lines takes into account the Brownian diffusion. (B) Corresponding Gaussian variance for three different ψ-values.

Figure 3

iMSD analysis of two representative conditions with same dynamic parameters (D = 0.75 10⁻³ μm² s⁻¹; v = 1.5 10⁻² μm s⁻¹; ϕ = −π/6) and different angular dispersions ψ₁ = π/4 (top panels), ψ₂ = 3π/2 (bottom panels). (A, G) Top view and (B, H) 3D view of the correlation function, (C, I) peak’s position as function of time (”×” for ξ₀(τ), ”+” for η₀(τ)), (D, J) time evolution of σ² from τ = 0 to τ = τ_m = 30 s and (E, F, K, L) circular sections g(ρ_∞, θ, τ), g(ρ_∞, θ, τ_m) for ρ_∞ = ω.

Figure 4

(A) Circular section of the correlation function at ρ_∞ = ω, τ = τ_m, for dynamics driven by same flow speed v and different angular dispersions ψ. Remarkable drift’s effects are manifest for low ψ-values. (B) Corresponding time evolution of σ², The parabolic contribution increases with ψ, complementarily to the peak’s shift. The black error bar shows the square correlation radius, obtained through Eq. 9. (C) output values of $a_{\sigma }^2$ and (D) relative differences from the input values of the dynamic parameters, as functions of ψ. Input arguments: D = 0.75 10⁻³ μm² s⁻¹; v = 1.5 10⁻² μm s⁻¹; ϕ = −π/6.

Figure 5

Output values of (A) diffusion coefficient and (B) flow speed as functions of ψ, obtained from STICS and iMSD. The vertical lines individuate ψ_c, the input parameters are shown as horizontal red and blue lines, respectively for D = 1.5 10⁻³ μm² s⁻¹ and v = 0.5 10⁻² μm s⁻¹.

Figure 6

(A) First frame of a simulated image-stack affected by slowly changing background. (B) Background intensity as a function of time: a Gaussian noise is added to a modulating sinusoid function of period T_b. (C) Intensity distribution over the image-stack, adopted to set the background filter. (D) Effects of background on the temporal correlation function and (E) corresponding curves after the filtering procedure. (F) Background’s effect on the Gaussian variance (T_b = 30 s). The presented dynamics is characterized by the following input parameters: D = 10⁻³ μm² s⁻¹; v = 1.5 10⁻² μm s⁻¹; ψ = π; ϕ = π/6.

Figure 7

(A) fluorescence-labeled cationic liposomes/DNA complexes in CHO cells. (B) Velocity maps over the entire image (yellow) and on single ROIs (cyan). The arrows indicate direction and modulus of the drift’s speed v⃗_ϕ and the circumferences have radius proportional to the speed modulus v. Origin of flow vectors are placed on the corresponding image center of mass. iMSD results are reported as peak’s shift (C) and time evolution of Gaussian variance (D). Both anisotropic and symmetric terms contribute to the characterization of motion.