Fig 1.
Multi-cellular protein interaction network of in vivo cross talk between macrophages and glomerular endothelial cells.
The protein interaction network between macrophages (gray area) and glomerular endothelial cells (pink area) is stimulated with static or dynamic glucose. The green oval is the input node, the blue ovals are the output nodes, and the white ovals are the regulatory nodes. Structural changes in glomerular endothelial cells are shown as blue squares. The black solid arrows are activating interactions, the red edges with dots at one end are inhibiting interactions, and the gray dashed arrows are interactions active for diabetic subjects. Open dotted arrows in orange and black represent negative and positive effects on fenestration size, respectively. Red circles indicate logic AND gates. An OR logic rule connects two or more edges to a subsequent node throughout the network unless indicated otherwise by an AND logic gate. The subscript “ec” denotes an intracellular species expressed in endothelial cells. IL-6, TNF-, IL-1
, and VEGF-A are protein levels expressed in the extracellular space. ROS, ROSec, VEGF-A (mRNA), and NO are expressed within the cells. The pJunction node represents the phosphorylated junction protein levels. Stress fibers and relaxed fibers represent different forms of actin fibers. AGE: advanced glycation end products. AKT: serine/threonine-specific protein kinases. Ca: calcium. eNOS: endothelial nitric oxide synthase. IL: interleukin. MLC: myosin light chain. MLCK: myosin light chain kinase. MLCP: myosin light chain phosphatase. NADPH: nicotinamide adenine dinucleotide phosphate. NF
B: nuclear factor kappa B. NO: nitric oxide. ONOO: peroxynitrite. PI3K: phosphoinositide 3-kinases. PLC-
: phospholipase C gamma. pMLC: phosphorylated myosin light chain. RAGE: receptor of advanced glycation end product. Rock: RhoA-associated kinase. ROS: reactive oxygen species. TLR: toll-like receptor. TNF-
: tumor necrosis factor-alpha. VEGF: vascular endothelial growth factor. VEGFR: vascular endothelial growth factor receptor. New nodes and interactions in the extended model compared to those in the previous model [27] are highlighted in Fig A in S1 Appendix.
Fig 2.
Simulated glucose input concentration profiles.
Simulated glucose input concentration profiles (black dashed curve on left axis) over 20 weeks using the linear fit for 2–6 weeks from Eq (1) and piecewise constant values of glucose at the means of the observed data in diabetic mice for 6–20 weeks. Dimensional glucose values G(t) are shown on the left axis, and normalized values of glucose reaction weight obtained using Eq (2) are shown on the right axis (black dotted curve). Glucose concentration data values are from Lee et al. [22] (blue circles) and Finch et al. [10] red triangles for male ob-/ob- mice. Data are shown as means ± standard deviations.
Fig 3.
Simulated glucose input concentration profiles (solid colorful lines) for a virtual mouse population (n = 100) to represent time-dependent inter-subject glucose variability.
Glucose was sampled n times in each time interval for 6–20 weeks by drawing from a normal distribution with mean and standard deviation from the data at the start of the corresponding time interval. The mean of the 100 profiles is shown as a solid black line. Glucose concentration data values are from Lee et al. [22] (blue circles) and Finch et al. [10] (red triangles). Data are shown as means ± standard deviations.
Table 1.
Parameters that modulate change in fenestration number and diameter.
Fig 4.
Simulated fenestration number and diameter.
A: Simulated fenestration number fitted against observed mean fenestration density (black circles) in diabetic mice [10]. B: Simulated fenestration diameter fitted against observed mean fenestration width (black circles) in diabetic mice [10]. Blue-shaded regions show the 95% credible intervals of the predictions. Data are shown as mean ± standard deviation (SD). Individual fenestration width and density are also reported for each diabetic mouse (open circles). Initial values for fenestration diameter and number were assumed to be the same as baseline control mean data values of fenestration width and density (red squares) for healthy mice in Finch et al. [10].
Fig 5.
Predicted dynamics of the species in the multi-cellular protein interaction network (Fig 1) simulated using the 100 G(t) trajectories (Fig 3) for the virtual mouse population as input.
Note that the means of the outputs from the 100 input glucose trajectories are shown in black, while the dynamic outputs for individuals cycle through MATLAB’s default color order.
Fig 6.
Ordered normalized sensitivity indices in Eq (6) with respect to fenestration number output expressed as percentages.
A: Sensitivity indices for species i when
was completely inhibited at the initial time. B: Sensitivity indices
for reaction j when Wj was completely inhibited at the initial time.
Fig 7.
Ordered normalized sensitivity indices in Eq (6) with respect to fenestration diameter output expressed as percentages.
A: Sensitivity indices for species i when
was completely inhibited at the initial time. B: Sensitivity indices
for reaction j when Wj was completely inhibited at the initial time.
Fig 8.
Simulated glucose input concentration profiles for time-dependent glucose control interventions.
For 6–20 weeks, the 100 G(t) trajectories (Fig 3) for the virtual mouse population were used as the inputs before and without intervention, and the means of the 100 profiles are plotted. The “No intervention” case (solid black line) is the glucose inter-subject variability scenario. In silico glucose control “intervention" was applied at 4 weeks (dotted black line) and 10 weeks (dashed gray line) by resetting glucose to its initial value . Glucose concentration data values are from Lee et al. [22] (blue circles) and Finch et al. [10] (red triangles). Data are shown as means ± standard deviations.
Fig 9.
Predicted changes in species in the multi-cellular protein interaction network (Fig 1) simulated using the time-dependent glucose control interventions (Fig 8) as input.
Predicted changes in A: activity and B: fenestration number and diameter from baseline without glucose intervention. Predicted changes in C: activity and D: fenestration number and diameter from baseline with glucose intervention applied at 4 weeks. Predicted changes in E: activity and F: fenestration number and diameter from baseline with glucose intervention applied at 10 weeks.
Fig 10.
Bar plots comparing the simulated glomerular endothelial cell fenestration number and diameter.
A: fenestration number and B: diameter at 20 weeks in the inter-subject glucose variability virtual mouse population without (gray bars) and with treatment by respective chemical agents (white bars). For the in silico treatment, each of the targeted species parameters () was reduced one-at-a-time by 100% at the initial time of 2 weeks. Observed number and diameter in healthy (blue bars) and diabetic (black bars) mice from Finch et al. [10] are also shown as mean ± standard deviation of the data. ***: p-value<0.001, ****: p-value<0.0001 for t-test comparison between data for healthy mice and model predictions in diseased virtual mice with or without treatment. **: p-value<0.01, ***: p-value<0.001, ****: p-value<0.0001 for t-test comparison between data for diabetic mice and model predictions in diseased virtual mice with or without treatment. Simulated results bars are shown as mean ± standard deviation across the virtual mouse population (n = 100).
Fig 11.
Structural effects over time as a result of the perturbation analysis for inhibiting sensitive parameters at 8 weeks.
After starting at their optimal values, each of the species parameters () and reaction parameters (Wj) was reduced one-at-a-time by 50%. A, B: Fenestration number output for perturbed parameters for sensitive A: species and B: reactions. C, D: Fenestration diameter output for perturbed parameters for sensitive C: species and D: reactions. Black curves (labeled as “No inhibition”) on each panel serve as the controls and show the structural effects without inhibition.