Fig 1.
a. Structure of a 24 subunit ferritin polymer cage, (reproduced from Ebrahimi et al. [43] without modification). b. Cartoon representing a single 24-subunit polymer FT cage illustrating the iron sequestration process broken up into a series of steps (as if the cage was cut in half and the dark grey rectangles signify the FT subunits with gaps for LIP transport into the cage cavity and the light grey representing the internal cavity that fills up with iron). The model represents the process of ferritin iron sequestration by approximation of the steps into four reactions, the first two of which are combined in the figure because they compose a reversible reaction. Oxidation represents the combined processes of ferrous (+2 charge, light blue) iron transport into ferritin through the three-fold pore, binding to the ferroxidase center located on H subunits, and the oxidation to the ferric state (+3 charge, dark blue, in the form of DFP), and unbinding from the ferroxidase (steps 1,2,3,4 respectively), with Reduction the reverse. Mineralization is the process of incorporating the two iron ions that are part of DFP into the mineral core (step 6). The rate of this process depends on the amount of iron already in the core. It proceeds as DFP that has unbound (step 4) from the ferroxidase reacts with the preexisting core and is incorporated into it. Nucleation represents a special case of mineralization, one where there is no preexisting core so it must be formed from several existing DFP molecules (step 5).
Table 1.
Model mathematical representation.
Shown below are the four reactions in the model, their stoichiometries, rate laws, and rate laws parameter values. The first two reactions, oxidation and reduction are parameterized from published data. Nucleation and mineralization were parameterized using parameter estimation.
Fig 2.
Model calibration and validation.
a. Calibration. Using data from Harrison 1974 [40], parameter estimation was performed to determine the parameters for mineralization and nucleation. Following the parameter estimation, the model produced output (black line) that was a good representation of the experimental data (blue circles). Conditions: 4 H-chains/FT, 2.32 μM FT, 470 Fe atoms per FT cage b-g. Validation. To validate the model, the model was run against four independent experimental conditions. For each experiment, the model parameters were preserved, only the initial concentrations were altered to match the experimental conditions. b. DFP formation over time (from Tosha 2008 [38] Fig 2B, Conditions: 24 H-chains/FT, 4.2 μM FT, 1–600 Fe atoms per FT cage), c. Iron addition and mineralization (from Zhao 2003 [21] Fig 2, Conditions: 4 H-chains/FT, 0.2 μM FT, 410 Fe atoms per FT cage). d and e. Mineralization from varied initial iron concentrations (from Fig 1 of Bou 2019 [39]), Conditions: 24 H-chains/FT, 0.5 μM FT. Each time course represents an experimental condition where the FT concentration is the same and the initial iron added was varied. From bottom to top, the amount of iron atoms added per FT cage was 42, 100, 200, 300, 400, 500. f. Iron addition and mineralization (from Zhao 2003 [21] Fig 3, Conditions: 24 H-chains/FT, 0.5 μM FT, 100 and then 700 and 700 Fe atoms per FT cage). g. Iron addition and mineralization (from Zhao 2005 [41] Fig 2B, Conditions: 4 H-chains/FT, 22 μM FT, 0–20 Fe atoms per FT cage).
Fig 3.
Iron atom per core effect on FT dynamics.
a. Mineralization rate over time as a function of iron APC. a series of simulations were run for which the initial ferritin concentration was 2.32×10-6M and iron added was 1.09×10−3 M, corresponding to 470 iron atoms per cage, while the initial iron content (APC) varied from 0 to 4300 (as indicated by the colorbar on the right). b. Core accumulation over time as a function of initial APC. From the same simulations that generated the plots in A, here the total core mineralization is plotted over time with the same variation in iron per cage of 0 to 4300 atoms. c. Maximum mineralization rate. Plotted is the maximum value for the mineralization rate as a function of iron atoms per cage. This is the maximum value from the curve in a over the entire time course. d. Time to sequestration and time to maximum mineralization rate. Plotted is the time taken to reach the maximum value for the mineralization rate shown in c. Also plotted is the time taken for 99% of the LIP in solution to be sequestered dependent on initial iron atoms per cage. For values over 3729 atoms per cage it took longer than the 25 second time course.
Fig 4.
Model simulation at the cell scale and analysis of FT concentration and iron per core in 2 factor tuning of FT buffering behavior.
a. Effect of FT concentration on buffering behavior. A series of simulations were run to determine the effect of FT concentration on the iron sequestration dynamics. Iron is added to the cytoplasm by setting LIP to 1μM at the simulation start and then set again at 400 seconds to 2μM. The curve shows the LIP remaining in solution over time in the presence of different FT concentrations (colorscale). b. Effect of FT concentration on initial LIP sequestration rate. The initial LIP sequestration rate across the same range of FT concentrations as in A is calculated following the addition of 1μM LIP. c. FT buffering of large LIP additions. A series of simulations were run to determine the LIP sequestration of larger LIP additions. Each curve indicates a simulation run at a FT concentration (5nM, 20nM, 50nM) and LIP concentration (2μM, 4.33μM, 6.66μM, 10μM).
Fig 5.
Iron release from FT after LIP reduction.
At time 400 second the LIP was eliminated (reduced to 0 M) and the resulting DFP and LIP concentrations are plotted as iron is liberated from FT. Each curve indicates a simulation run at a FT concentration (5nM, 20nM, 50nM) (darker color is a higher FT concentration).
Fig 6.
Model simulation at the cell scale and analysis of FT concentration and iron per core in 2 factor tuning of FT buffering behavior.
Effect of iron per cage on buffering behavior. A series of simulations were run to determine the effect of varying the initial core size (APC) so that the cages at an identical FT concentration (5x10-9 M) had different iron content from 0 to 4300 APC. a shows the curves in 2D with LIP remaining after a 2.5 μM LIP addition at time 0; in b the APC is added as a 3rd dimension for visual clarity. Simultaneous variation of FT concentration and APC on buffering behavior. A series of runs at 3 FT concentrations were run 5x10-9 M (red), 2x10-8 M (purple), 5x10-8 M (blue). For c and d each run in addition to the FT concentration, the APC was varied between 0 and 4300 as well.
Fig 7.
Subunit composition effect on FT iron sequestration dynamics.
The model contains a parameter H that can be varied to incorporate differences in subunit composition of a population of FT-cages versus another and the effect of the composition on the rate laws of oxidation and nucleation. H represents the number of H subunits and can be between 0 (L homopolymer) and 24 (H homopolymer). We ran 13 simulations with the number of H subunits in the FT cages increasing from 0 to 24 in increments of 2. Then iron sequestration behavior was assessed by tracking a) LIP b) APC and c) nucleation rate over time.
Fig 8.
Model dynamics with FT core iron release.
Release was incorporated into the model and balanced by expression as noted above to reach an equilibrium FT concentration of 5nM. The model was then run for 10,000 seconds to let the system approach steady state (where LIP did not change over time). Then LIP was doubled and subsequently halved (at time 25,000). a. The amount of LIP (blue), core (green), DFP (orange) and FT-cage (red) concentrations are plotted over time. For analyzing behavior over the long term and response to repeated iron challenges (b—e), three increasing expression rate values (3.075x10-14, 6.015x10-14, 1.203x10-13) were chosen for the long term sequestration analysis (“low”, “mid”, “high” curve labels respectively). These rates corresponded to equilibrium concentrations of FT of 2.56nM, 5nM, and 10nM. For simulation every 105 s (about 1 day) the LIP was increased by 0.5μM, a small physiologic dose. The b) LIP and c) APC were plotted corresponding to the model with each of these expression rate values over time. The reverse was also performed, where every 105 s the LIP was reduced to 0 and again the d) LIP and e) APC were plotted.
Fig 9.
To analyze the effect of substituting the model presented in this work with the FT representation of a previous model, a simulation from the previous model was run and the behavior of FT associated iron compared. For simulation, all parameters of both models are kept the same, except for the amount of FT in the core (due to the new model’s dependence of mineralization on APC). At time 0, the FT concentration was 1.66 nM and LIP was increased to 1.3 μM. Tracked was the newly accumulated FT associated iron after the LIP increase, represented differently in each, but representing the same FT core. a. FT iron (orange) accumulation over time in original hepatocyte model from Mitchell et al. 2013 [33] b. New FT core (blue) and core plus DFP (black) accumulation over time in hepatocyte with new FT model. Final FT concentrations were 37.5nM and 15.8nM respectively.