Understanding intracellular transport processes pertinent to synthetic gene delivery via stochastic simulations and sensitivity analyses

Abstract

A major challenge in synthetic gene delivery is to quantitatively predict the optimal design of polymer-based gene carriers (polyplexes). Here, we report a consistent, integrated, and fundamentally grounded computational methodology to address this challenge. This is achieved by accurately representing the spatio-temporal dynamics of intracellular structures and by describing the interactions between gene carriers and cellular components at a discrete, nanoscale level. This enables the applications of systems tools such as optimization and sensitivity analysis to search for the best combination of systems parameters. We validate the approach using DNA delivery by polyethylenimine as an example. We show that the cell topology (e.g., size, circularity, and dimensionality) strongly influences the spatiotemporal distribution of gene carriers, and consequently, their optimal intracellular pathways. The model shows that there exists an upper limit on polyplexes' intracellular delivery efficiency due to their inability to protect DNA until nuclear entry. The model predicts that even for optimally designed polyethylenimine vectors, only approximately 1% of total DNA is delivered to the nucleus. Based on comparison with gene delivery by viruses, the model suggests possible strategies to significantly improve transfection efficiencies of synthetic gene vectors.

FIGURE 1

Computer representation of human skin fibroblasts (a) in vitro, where the cell is represented as a two-dimensional object and (b) in vivo, where the cell is represented by a three-dimensional structure. Green and red objects represent endosomes and lysosomes respectively. Thin yellow lines represent microtubules (MTs). The microtubule-organizing center (MTOC) is randomly located in the vicinity of the nucleus. For clarity, we use fewer endosomes, lysosomes, and MTs to render the reconstructed cells than in simulations. Two regions of the three-dimensional cell are magnified and shown in panels c and d.

FIGURE 2

Gene delivery pathway of polyplexes. Polyplexes are internalized by endocytosis. They are immediately delivered to endosomes and subsequently to lysosomes. To gain entry to the nucleus, the polyplexes must escape from endosomes or lysosomes. Once inside the cytoplasm, the polyplexes unpack to release the DNA for successful nuclear entry. Ultimately, the exogenous DNA is transcribed, and gene products are synthesized. The biophysical states S and the rates of transition between them are shown in the figure.

FIGURE 3

Transport properties of endosomes. (a) Distribution of the duration of runs of endosomes in the plus (solid circles) and minus (open circles) directions and (b) distribution of the frame-to-frame velocities in plus (solid circles) and minus (open circles) directions. The vertical coordinate indicates the frequency of occurrence of an event, i.e., the probability of observing a certain run-length (a) or a certain velocity (b).

FIGURE 4

Intracellular spatial distribution of lysosomes and transfer of PEI-DNA from endosomes to lysosomes. (a) Fluorescent micrograph of lysosomes labeled by incubation of human dermal fibroblasts with fluorescent dextran for 2 h followed by a 22-h chase in culture medium. The nuclear and cell membrane are traced for clarity. Inset shows typical clusters of perinuclear lysosomes. (b) Spatial distribution of lysosomes represented by p(r), the probability of finding a lysosome at a distance r from the nucleus. (c) Gradual delivery of PEI²⁵-DNA vectors from endosomes to lysosomes. The ordinate is the fraction of total intracellular PEI²⁵-DNA vectors that colocalize with LAMP1 positive structures (lysosomes) at different times post-transfection. Lysosomal delivery is seen to be substantially complete at 24 h post-transfection. The shaded line is a first-order kinetic fit on the data yielding k_transfer = 1/500 min⁻¹.

FIGURE 5

Model validation. (a) Displacement probability p(x,t) of a particle engaging in motor-assisted transport along a filament at t = 25 s (solid line, exact solution; open circles, simulation) and t = 100 s (dashed line, exact solution; solid circles, simulation). (b) Average mean-squared displacement for stochastically generated trajectories (solid line) and the experimentally measured trajectories (triangle). A crossover from subballistic to diffusive regime occurs between t = 10–100 s.

FIGURE 6

Comparison of model predictions (lower panel) of spatiotemporal distribution of PEI-DNA complexes to experimental data (upper panel). PEI-DNA complexes are labeled with Oregon green (green) and lysosomes are immunolabeled with rhodamine-X labeled secondary antibody (red). The yellow regions represent PEI-DNA vectors that colocalize with lysosomes. The same cells are reconstructed using simulations and presented in lower panel. The three cells correspond to (a, b) 30 min, (c, d) 4 h, and (e, f) 11 h post-transfection.

FIGURE 7

Validation of the model against experimental measurement of spatio-temporal distribution of PEI^25kDa-vectors. (a) Normalized local concentration c(r,t) of vectors measured experimentally (symbols) and predicted by the model (lines) at 10 min (circles), 2 h (squares), and 24 h (triangles). The abscissa is r, the distance from the nucleus. The distributions are sampled from 20 cells. (b) The temporal evolution of vector concentration in the supranuclear region (squares) and the perinuclear region (circles). The perinuclear region is defined as a region of width 2 μm around the nucleus. The lines are the predicted distributions.

FIGURE 8

Likelihood of successful DNA delivery. (a) The value Φ(r,t), the probability that a vector, which escapes at a distance r from the nucleus at time t, will reach the nucleus. The probability is evaluated at 24 h after the occurrence of the escape event (r > 0, cytoplasmic region; r < 0, supranuclear region). (b) The value Θ(t_e), the probability that a vector, initially located in the supranuclear (solid) or cytoplasmic (dotted) region, completes DNA delivery to the nucleus at 24 h after escape from endosome or lysosome at time t.

FIGURE 9

Delivery efficiency in two-dimensional cells Ψ_{in vitro} as a function of k_escape, k_tr, and k_unpack. The value Ψ_{in vitro} measures the fraction of vectors that successfully deliver DNA to the cell nucleus within 24 h post-transfection. The minimum and maximum values of Ψ_{in vitro} are 0.8 × 10⁻⁷ (blue) and 2 × 10⁻² (red), respectively. The values k_escape, k_tr, and k_unpack are the rates of escape from endocytic vesicles, transfer from endosomes to lysosomes, and vector unpacking, respectively. Slices of the function at different values of (a) k_unpack and (b) k_tr.

FIGURE 10

Spatiotemporal distribution of vectors in three-dimensional cells. Predicted spatial distribution of PEI^25kDa-DNA complexes in a three-dimensional cell at 10 min (solid), 4 h (shaded), and 24 h (dotted) post-transfection. is the probability that a vector is located at distance r from the nucleus at time t in a three-dimensional cell.

FIGURE 11

Delivery efficiency in three-dimensional cells Ψ_{in vivo} as a function of k_escape, k_tr, and k_unpack. The color indicates Ψ_{in vivo}. Ψ_{in vivo} denotes the fraction of vectors that successfully deliver DNA to the cell nucleus within 24 h post-transfection. The minimum and maximum values of Ψ_{in vivo} are 0.8 × 10⁻⁷ (blue) and 3.7 × 10⁻³ (red), respectively. The values k_escape, k_tr, and k_unpack are the rates of escape from endocytic vesicles, transfer from endosomes to lysosomes, and vector unpacking, respectively. Figure shows slices of the function at different values of (a) k_unpack and (b) k_tr.

FIGURE 12

Effect of cell shape and size on the delivery efficiency Ψ_{in vitro} for dermal fibroblasts in culture. The color indicates Ψ_{in vitro}. The ratio between the maximum and minimum delivery efficiency is 6.2. The delivery efficiency increases with decreasing size and circularity. Low circularity often provides higher access to nucleus, hence the higher transfection efficiency. The circles denoted by A–C show three extremes in the circularity-size space that are captured by the cell population used. Note that k_escape = 0.15 h⁻¹, k_tr = 0.1 h⁻¹, k_degL = 0.042 h⁻¹, D_DNA = 10⁻³ μm²/s, k_deg-cyto,DNA = 1 h⁻¹, k_nuc = 1/4 h⁻¹, and k_unpack = 0.25 h⁻¹.

FIGURE 13

Design strategies to improve PEI^25kDa-DNA polyplexes. (a) Ratio of different polymer-dependent parameters of the optimal solution to those of PEI^25kDa for in vitro (solid bars) and in vivo (hatched bars) and (b) Ψ_{in vivo} as a function of k_unpack and k_escape for k_tr = 1/500 min⁻¹ (for PEI^25kDa). The position of PEI^25kDa is also indicated (yellow star). The arrow shows the trajectory to be followed to arrive at the optimum, assuming k_tr is held constant.