Particle Simulation of Oxidation Induced Band 3 Clustering in Human Erythrocytes

Oxidative stress mediated clustering of membrane protein band 3 plays an essential role in the clearance of damaged and aged red blood cells (RBCs) from the circulation. While a number of previous experimental studies have observed changes in band 3 distribution after oxidative treatment, the details of how these clusters are formed and how their properties change under different conditions have remained poorly understood. To address these issues, a framework that enables the simultaneous monitoring of the temporal and spatial changes following oxidation is needed. In this study, we established a novel simulation strategy that incorporates deterministic and stochastic reactions with particle reaction-diffusion processes, to model band 3 cluster formation at single molecule resolution. By integrating a kinetic model of RBC antioxidant metabolism with a model of band 3 diffusion, we developed a model that reproduces the time-dependent changes of glutathione and clustered band 3 levels, as well as band 3 distribution during oxidative treatment, observed in prior studies. We predicted that cluster formation is largely dependent on fast reverse reaction rates, strong affinity between clustering molecules, and irreversible hemichrome binding. We further predicted that under repeated oxidative perturbations, clusters tended to progressively grow and shift towards an irreversible state. Application of our model to simulate oxidation in RBCs with cytoskeletal deficiency also suggested that oxidation leads to more enhanced clustering compared to healthy RBCs. Taken together, our model enables the prediction of band 3 spatio-temporal profiles under various situations, thus providing valuable insights to potentially aid understanding mechanisms for removing senescent and premature RBCs.


Detailed description of human erythrocyte band 3 clustering model.
The main body of our band 3 clustering model is based on a previously published kinetic model of human erythrocyte (RBC) metabolism [1]. The minimal reactions associated with the antioxidant pathway shown below, were extracted from the original whole RBC metabolism model.  Table 1. Below (Table 2) is a list of processes that structure the model. Parameter values were taken from [3].
Parameter values were taken from [4].

OX
(S5) S: substrate of the reaction Parameter Value The parameter value was adjusted to achieve the appropriate steady-state concentration of metabolites.

1-3. Comparison of minimal model and model with whole RBC metabolism
The minimal model with the above reactions and the whole RBC model both showed similar steady state values for metabolites.

1-4. Descriptions of diamide-mediated reactions
The following reactions represent the reactions that occur when the RBC is treated with diamide, thiol group oxidant. Simulation settings were set to 30% hematocrit, similar to the experimental study ( [5]), by constructing a RBC compartment (where internal diamide is present) nested within a larger environment compartment (where external diamide, or ext_diamide is present). A was set to 0 at steady state, and was set to 1 to model the incubation of cells with diamide.
Once inside the cell, diamide rapidly reactions with GSH to form GSSG. (main text, When first simulating the model with the given reactions, we found that GSH was only slightly decreased, and it quickly returned to its initial levels (Figure 2, grey).
Since the rate of direct diamide reduction with GSH was high, we assumed that there was an alternative diamide-mediate pathway that created a long-lasting effect on GSH metabolism.
A survey on the effects of diamide revealed the following: • A significant amount of GSH may be reversibly bound to protein, resulting in formation of mixed disulfides between GSH and protein sulfhydryl groups to form S-glutathionylated proteins (PSSG), under oxidative stress ([8]) • The formation of bonds is reversible after removal of oxidative stress ([9]) • In RBCs, diamide has been shown to induced mixed disulfide bonds between GSH and Hb, and also membrane skeletal proteins ( [10], [11]) Given the above, we decided to incorporate these effects of diamide into the model so that there would be two pathways of GSH consumption. The reaction scheme is as shown below.
As the parameters were not available in literature, we estimated these parameters by conducting a parameter analysis and comparing it with the time course observed from the previous experiment for the control RBC treated with diamide ( [5]).

Detailed description of the band 3 clustering model incorporating spectrin interactions
The prototype model for band 3 clustering was extended to include the cytoskeletal components that characterize the RBC membrane.

2-1. Descriptions of modeling the cytoskeletal spectrin network compartment
In the model incorporating the spectrin cytoskeletal network, in addition to regular vacant voxel species, we assigned certain vacant voxel species to be specific to holding spectrin/bound band 3 species (main text Figure S2). Therefore, for each band 3 state  The reaction scheme, equations, and parameters for the hop-diffusion reaction are given below.
freeBand3 + spectrin p ! → ! Spectrin_Band3 (S11) Spectrin_Band3 k ! → ! Spectrin+Band3 (S12) Parameter Value Reference p 0.008 fitted to [12] k 100 M s -1 fitted to [12] Once the RBC is treated with diamide, band 3 species (included BoundBand3) are oxidized, phosphorylated, and BoundBand3 become freely diffusing Band3phos molecules which diffuse away from their original positions. Since the tethering BoundBand3 is absent and replaced by a vacant compartment (vertex), the neighboring spectrin is also removed form its original position and replaced by a vacant compartment (edge). Thus oxidation induces a zipper like removal of the spectrin network. The reaction scheme, equations, and parameters for these reactions after oxidation are given below.
spectrin + vertex k1 ! → !! edge (S13) edge + spectrin k 2 ! → !! edge (S14) Parameter Value Reference k1 0.01 approximated k2 0.0001 approximated By incorporating these reactions representing the properties of the membrane at steady state, and the dissociation of the spectrin cytoskeleton upon oxidative treatment, we were able to more closely reproduce the effects of oxidation in silico, and assess the how band 3 clustering may be regulated by the spatial organization of the RBC membrane.