Application of circuit simulation method for differential modeling of TIM-2 iron uptake and metabolism in mouse kidney cells

Abstract

Circuit simulation is a powerful methodology to generate differential mathematical models. Due to its highly accurate modeling capability, circuit simulation can be used to investigate interactions between the parts and processes of a cellular system. Circuit simulation has become a core technology for the field of electrical engineering, but its application in biology has not yet been fully realized. As a case study for evaluating the more advanced features of a circuit simulation tool called Advanced Design System (ADS), we collected and modeled laboratory data for iron metabolism in mouse kidney cells for a H ferritin (HFt) receptor, T cell immunoglobulin and mucin domain-2 (TIM-2). The internal controlling parameters of TIM-2 associated iron metabolism were extracted and the ratios of iron movement among cellular compartments were quantified by ADS. The differential model processed by circuit simulation demonstrated a capability to identify variables and predict outcomes that could not be readily measured by in vitro experiments. For example, an initial rate of uptake of iron-loaded HFt (Fe-HFt) was 2.17 pmol per million cells. TIM-2 binding probability with Fe-HFt was 16.6%. An average of 8.5 min was required for the complex of TIM-2 and Fe-HFt to form an endosome. The endosome containing HFt lasted roughly 2 h. At the end of endocytosis, about 28% HFt remained intact and the rest was degraded. Iron released from degraded HFt was in the labile iron pool (LIP) and stimulated the generation of endogenous HFt for new storage. Both experimental data and the model showed that TIM-2 was not involved in the process of iron export. The extracted internal controlling parameters successfully captured the complexity of TIM-2 pathway and the use of circuit simulation-based modeling across a wider range of cellular systems is the next step for validating the significance and utility of this method.

Keywords: TIM-2; circuit simulator; export; ferritin; iron; model; storage; uptake.

Figure 1

TIM-2 pathway model of the TIM-2 receptor, endosome formation, HFt degradation, and iron release into the iron labile pool. Iron is subsequently either stored in endogenous HFt or exported to the media. Iron uptake by the TIM-2 receptor occurs at the cellular membrane. ++ represents Fe (ferrous state), and ++ with ovals represents Fe-HFt. Unshaded ovals are for external HFt, and shaded ovals are for endogenous HFt. The question marks (?) represent pathways that do not have any direct experimental support.

Figure 2

An example circuit generated by ODE-to-circuit conversion. The component on the left is a current-control current source (CCCS), an ideal element for current scaling. The scaling factor G = 1 for the element mirrors the current, representing iron atoms in a TIM-2/ferritin complex. The current inputs into a capacitor are to model the state of iron accumulation. At a linear release condition, the stored charge in capacitor leaks through the resistor RR7, modeling the release of iron. The current is then mirrored again on the right side of the circuit to input into another state representing iron atoms in a TIM-2/ferritin complex.

Figure 3

Example circuits of nonlinear behavior. (A) Linear to saturation model; (B) Constant to suppression model.

Figure 4

View of ADS simulation bench for simulation of TIM-2 pathway model. (A) Simulation setup defines the time duration and resolution; (B) Variable setup defines parameters and their range for optimization or tuning; (C) Initial condition and environment (external source) as applied to the cell subcircuit through wire connections; (D) Optimization setup of optimization methods and iteration time; (E) Goals for optimization.

Figure 5

Comparison of iron uptake rates between laboratory data and simulation. Cells were harvested at different time points over a 2-h period and ⁵⁵Fe amounts in cytosol fractions were counted. Data shown are means and standard deviations for triplicate replication of the experiment. The experiment was performed in triplicate.

Figure 6

Comparison of iron storage rates between laboratory data and simulation. Cells were treated with biotinylated HFt loaded with ⁵⁵Fe for various time points and the ⁵⁵Fe amounts in biotinylated and non-biotinylated fractions were counted. Data shown are means and standard deviations for triplicate replication of the experiment. The experiment was performed in triplicate.

Figure 7

Comparison of iron export rates between laboratory data and simulation. Cells that had been preloaded with Tf-⁵⁵Fe were washed and changed into normal growth media. Media were collected at different time points over a 48 h period and ⁵⁵Fe amounts in media were counted. Data shown are means and standard deviations for triplicate replication of the experiment. The experiment was performed in triplicate.