(a) Two-dimensional sketch of a parasite with a directional vector 𝐧 from the parasite’s back at rx=1.5μm to its apex at rx=0. (b) Three-dimensional triangulated surfaces of a RBC (red) and a parasite (blue). Bonds between the parasite and RBC can form within the contact zone which is illustrated by a magnified view, where discrete receptor-ligand interactions (or bonds) are sketched. A bond can form with a constant on-rate kon and break with a constant off-rate koff.
(a) A time instance of parasite motion at RBC membrane from an experimental video (Weiss et al., 2015) (top) and simulation (bottom), see also Video 1. To obtain the distribution of merozoite fixed-time displacements, the marked parasite (red circle) is tracked over the course of its interaction with the RBC membrane. (b) Comparison between experimental (20 samples) and simulated (100 samples) fixed-time displacements (Δd) of the parasite at RBC membrane, which is normalized by the effective RBC diameter D0=A0/π calculated from the membrane area A0. By adapting the interaction parameters, the displacement distribution in simulations is calibrated against the experimental distribution. The resulting reference parameters for our model can be found in Table 2. (c) Mean squared displacement (MSD) of a parasite from simulations as a function of time. The black solid line marks a diffusive regime with MSD∼t. Note the subdiffusive dynamics for short times, less than about 1s.
Source data for graphs shown in Figure 2(b,c).
(a) Sketch of apex distance dapex and alignment angle θ. The apex distance dapex is defined as a distance (magenta line) between the parasite’s apex and the closest vertex of RBC membrane. The alignment angle θ corresponds to the angle between the parasite’s directional vector (black arrow) and the normal vector 𝐧face (green arrow) of a triangular face whose center is closest to the apex. Note that the angle π-θ is drawn in the plot. (b and c) Probability distributions of the apex distance dapex/D0 and the alignment angle θ/π. Data are obtained for parameters shown in Table 2, and accumulated starting from an initial adhesion contact (i.e., formation of a few bonds). The dashed line in the apex distance distribution indicates the cutoff 21/6σ of repulsive LJ interactions. Note that a good parasite alignment requires small values of dapex/D0 and values of θ/π close to unity.
Source data for graphs shown in Figure 3b,c and Figure 3—figure supplement 1.
Probability distributions of (a) the apex distance dapex/D0, and (b) the alignment angle θ/π. The dashed line in the apex distance distribution indicates the cutoff 21/6σ of repulsive LJ interactions.
(a) Two-dimensional probability map as a function of dapex and θ. Each bin represents a single alignment state and the color corresponds to probability of that state. The dark green area (dapex/D0≤0.036 and θ/π≥0.8, compare with Equation 4) represents the criteria for a successful alignment. The black dashed line corresponds to the cutoff 21/6σ of repulsive LJ interactions. (b) Distribution of alignment times ta obtained from 86 statistically independent DPD simulations. ta is defined as a time interval starting from an initial adhesive contact (i.e., formation of a few bonds) to the instance when the alignment criteria for dapex and θ in Equation 4 are met. The average alignment time is equal to ⟨ta⟩≃9.53 s. (c) Alignment time distribution from MC sampling using the probability map in (a). The alignment time is defined as a number of MC steps needed to satisfy the alignment criteria, as the MC procedure does not have an inherit timescale. Note that the sample size in MC modeling (8000 trajectories) is much larger than that in (b).
Source data for graphs shown in Figure 4a–c.
Temporal changes in the number of bonds are shown for both long and short bond types. The dashed lines in the bottom plot correspond to the alignment criteria in Equation 4. For all quantities, the corresponding averages and variances represented by box plots are depicted on the right.
Source data for graphs shown in Figure 5 and Figure 5—figure supplements 1 and 2.
(a) Average total number of bonds between the merozoite and RBC as a function of the distance dcm between their centers of mass. (b) Illustration of parasite adhesion at the RBC rim (marked by I) and in the dimple (II). The parasite forms more bonds in the dimples (position II) than at the RBC rim (position I).
Since the off-rate controls the lifetime of bonds, a smaller off-rate results in a stronger adhesion, a lower parasite displacement, and a faster alignment time.
Source data for graphs shown in Figure 6a–c and Figure 6—figure supplement 1.
(a) RBC deformation energy and (b) the number of short and long bonds as a function of λ/λref. λref corresponds to the reference case with parameters given in Table 2. Note that both λlong and λshort are changed by the same factor with respect to their λref values. Here, the bond kinetic rates are konshort=290.3τ-1, konlong=36.3τ-1, and koff=72.6τ-1.
Source data for graphs shown in Figure 7a,b and Figure 7—figure supplement 1.
(a) Number of short and long bonds and (b) parasite alignment times as a function of ρlong/ρpara. Note that ρlong+ρshort=ρpara remains constant in all simulations. Here, the bond kinetic rates are konshort=290.3τ-1, konlong=36.3τ-1, and koff=72.6τ-1. In case of ρlong/ρpara=0.1, parasite alignment time could not be computed through the MC sampling, since merozoite alignment has never occurred in direct simulations.
Source data for graphs shown in Figure 8a,b and Figure 8—figure supplements 1 and 2.
(a) Deformation energy, (b) the number of bonds, (c) apex distance, (d) alignment angle, and (e) fixed-time displacement of the merozoite for the three cases: (1) ρlong/ρpara=1 and koff/konlong=2, (2) ρlong/ρpara=0.4 and koff/konlong=2 (the reference case), (3) ρlong/ρpara=1 and koff/konlong=0.25.
Note that for a rigid RBC with koff/konlong=1, parasite alignment time could not be computed through the MC sampling, as the alignment criteria have never been met in direct simulations.
Source data for graphs shown in Figure 9a,b.
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koff/konlong=2. See Figure 2a.
The effective RBC diameter D0=A0/π sets a basic length, the thermal energy kBT defines an energy scale, and RBC relaxation time τ=ηD03/κ sets a time scale in the simulated system, where A0 is the RBC surface area, κ is the bending rigidity, and η is the fluid dynamic viscosity. The values of bending rigidity κ, 2D shear µ and Young’s Y moduli are chosen such that they correspond to average properties of a healthy RBC. Parameters σ and ϵ correspond to RBC-parasite excluded-volume interactions represented by the purely repulsive LJ potential in Equation 11.
The parameter values in simulations are given in terms of the length scale D0, energy scale kBT, and timescale τ=ηD03/κ. The densities of long and short ligands are given in terms of parasite vertex density ρpara≃270μm−2. Note that ρlong+ρshort=ρpara in all simulations.