Fig 1.
The membrane skeleton in healthy and infected red blood cells.
(A) Left: schematic representation of a cut through a healthy RBC with a biconcave shape. Right: closeup of the coupling between the actin-spectrin network and the lipid bilayer. The actin protofilaments of the junctional complexes bind to glycophorin C (GPC) and ankyrin binds to anion exchanger 1 (AE1, also known as band 3). (B) Left: schematic representation of the late stage of the malaria infection, when the RBC has changed to a spherical shape and adhesive knobs have formed on its surface. Right: closeup of the internal structure of the knobs, with a spiral structure at the base, the PfEMP1 adhesion receptors in the membrane at the top and KAHRP-molecules inbetween. Actin is mined from the junctional complexes and forms long filaments often connected to the Maurer’s clefts.
Fig 2.
Particle-based model for the RBC cytoskeleton.
(A) Schematic of the spectrin tetramer structure at the top and implementation in the simulation at the bottom. Differently coloured beads have different properties that represent the interactions of the spectrin filaments with actin, ankyrin and KAHRP. (B) Implementation of dynamic actin filaments in the simulations. The top filament can polymerize at both ends with different rates at the barbed (b) and pointed (p) ends. For the filament at the bottom the polymerization is blocked, since the capping proteins adducin (a) and tropomodulin (t) are attached. (C) The potentials used in the simulations are plotted against particle separation. (D) The initial configuration of a typical simulation is shown as a projection along the z-direction. The simulation box has periodic boundaries and a size of 140 × 242.48 × 100 nm−3. G-actin particles are shown in grey. An example simulation can be seen in the S1 Movie. (E) Equilibrated state of the network.
Table 1.
Values for collision radii, reaction radii and diffusion constants.
Fig 3.
(A) Spectrin properties are tested by examining the end-to-end distance exemplified by the double arrow. (B) The root-mean-square value of the end-to-end distance is calculated for varying filament length. Simulations with an angle potential and excluded volume (wine) are compared to ones without angular confinement in red and simulations of ideal chains (i.e. no angle or excluded volume interactions) in orange. Additionally, we plot the analytic expression for the WLC (wine), the Flory theory (red) and the freely-joined chain (orange). (C) Capped actin filaments of different lengths. (D) The orientation of actin filaments within a network is quantified by the in-plane angle (orientation within the membrane) and the out-of-plane angle (angle in z-direction). These are plotted as a function of shear of the network. (E) The temporal evolution of actin filament average length is plotted for different initial values of G-actin concentration. The solid line shows the data from simulations containing capping proteins and the dotted lines show data from simulations without capping proteins. Each line corresponds to one simulated network with 46 actin filaments. The dashed vertical line indicates the time point for which the distributions are shown in F. (F) The smoothed probability distributions of the filament lengths at time 25 μs are shown for all concentrations. At the top the data is shown for simulations without capping proteins and at the bottom with capping proteins.
Fig 4.
(A) Snapshot of the simulation at shear 1.0 in the x-direction. Junctional points are modelled as single actin particles. (B) Same as in a but now the junctions are modelled as full actin filaments. (C) Examples of actin filaments at different lengths within the network. (D-H) Stress is plotted against shear extracted from simulations with a shear rate of 3 ⋅ 105 s−1. Each line corresponds to the average of 10 simulations. In D and G single particles are used as actin junctions whereas in E and H the proper actin filaments are implemented. In D and E the spectrin filaments are modelled without angle potentials and the anchoring sites are free to diffuse in the bilayer plane. In G and H the spectrin angle potential constant has a strength of 4.28 kJ mol−1 and the anchoring sites possess a reduced diffusion due to anchoring in the bilayer. (F) The stress response to shearing is plotted for different average filament lengths as indicated in the legend. Sheared networks are taken from all different concentrations and time points of simulations with capping proteins. The black line is for a perfect network with exactly N = 6 actin beads per filament and serves as a reference. (I) The final stress from C is now plotted against the average filament length with the colours indicating the different initial concentrations as shown in the legend.
Fig 5.
Effects of network connectivity on shear response.
(A) Schematic representation for the network set-up. The yellow bars represent actin filaments and red circles indicate where an actin filament is missing. The black lines show the initialization positions of spectrin filaments. (B) Final configurations of the simulated networks at a shear of 1. The colors of the particles are the same as shown in Fig 2. (C) The stress-shear response is shown for networks with different connectivity. The black line corresponds to the perfect hexagonal network with six spectrins per node and the yellow line shows the response of a network with three spectrins per node. Additionally, some networks were simulated where four/six wholes where bridged with six/nine long spectrin filaments. (D) Here the effect of missing actins and spectrin filaments is analysed. Either only the actin nodes were taken away (-4/6 actins) or the whole hexagonal element including the spectrins (-4/6 hexagons). Again, this is compared to the perfect hexagonal lattice response in black.
Fig 6.
Effect of KAHRP clusters in actin-spectrin network.
(A) Snapshots of equilibrated networks for the interaction energies indicated above each image. KAHRP particles are shown in grey and some KAHRP clusters are indicated by rectangles and shown as zoom-ins. G-actin particles are not shown here. (B) Fraction of clusters that are located at actin filaments in contrast to other cytoskeletal subunits. The value is calculated for different interaction energies with actin and ankyrin. (C) Shear response of KAHRP containing networks for different KAHRP positioning. (D) A simple spring model was set up to understand the shear-reasponse of the KAHRP-containing cytoskeletal networks. (E) The effective spring constant is plotted according to our spring model.
Fig 7.
Comparison of experimental and simulated pair cross-correlations.
(A) STED images of an exposed RBC membrane at the trophozoite stage (28–36 hours post malaria infection). Red and green fluorescence signals correspond to KAHRP and ankyrin sites on the RBC membrane. (B) Pair cross-correlation (PCC) between KAHRP and ankyrin computed using the two-color images obtained at different hours post malaria infection. (C) PCC between KAHRP and N-terminus of β-spectrin. Images and PCC values in (A,B) are taken from [35]. (D) KAHRP (red) and ankyrin (green) fluorescence signal is constructed from location points obtained from simulations (overlaid white points). (E) PCC between KAHRP and ankyrin is computed from two-color images generated from simulations for different binding energy between KAHRP and actin as indicated by the color bar. (F) Same as (E) for the KAHRP and N-terminus of spectrin PCC. (G) The map shows PCC values at zero distance for KAHRP-actin pairs (top panel) and KAHRP-ankyrin pairs (bottom panel) at different binding rates between KAHRP and ankyrin/actin sites for average actin filament length 24 nm. The white dots mark the cases where a peak is observed at a finite distance. (H) and (I) Same as (G) for average actin filament length 36 nm and 48 nm respectively.