Effect of malaria parasite shape on its alignment at erythrocyte membrane
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Evaluation Summary:
This manuscript studies the alignment of malaria parasites (merozoites) at the surface of red blood cells (RBCs), a key element of their reproduction cycle during the blood stage of the disease. Building on a computational model the authors developed previously, which incorporates the stochastic nature of RBC deformations and adhesive bonds between the merozoite and RBC, it is demonstrated that parasite shape plays a key role in its alignment dynamics. In particular, the authors shed new light on the egg-like shape typically observed in Plasmodium merozoites, which has important implications for how effectively the parasite can survive and multiply.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Abstract
During the blood stage of malaria pathogenesis, parasites invade healthy red blood cells (RBC) to multiply inside the host and evade the immune response. When attached to RBC, the parasite first has to align its apex with the membrane for a successful invasion. Since the parasite’s apex sits at the pointed end of an oval (egg-like) shape with a large local curvature, apical alignment is in general an energetically unfavorable process. Previously, using coarse-grained mesoscopic simulations, we have shown that optimal alignment time is achieved due to RBC membrane deformation and the stochastic nature of bond-based interactions between the parasite and RBC membrane (Hillringhaus et al., 2020). Here, we demonstrate that the parasite’s shape has a prominent effect on the alignment process. The alignment times of spherical parasites for intermediate and large bond off-rates (or weak membrane-parasite interactions) are found to be close to those of an egg-like shape. However, for small bond off-rates (or strong adhesion and large membrane deformations), the alignment time for a spherical shape increases drastically. Parasite shapes with large aspect ratios such as oblate and long prolate ellipsoids are found to exhibit very long alignment times in comparison to the egg-like shape. At a stiffened RBC, a spherical parasite aligns faster than any other investigated shape. This study shows that the original egg-like shape performs not worse for parasite alignment than other considered shapes but is more robust with respect to different adhesion interactions and RBC membrane rigidities.
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Author Response
Reviewer #1 (Public Review):
[...] The manuscript is excellently written and discusses the simulation results clearly and succinctly. The resolution of the simulations is very impressive and yields unprecedented insight into the effect of merozoite shape on alignment dynamics, which has important implications for how effectively the parasite can survive and multiply. The conclusions reached by the authors are certainly justified by the simulation data. In particular, the authors are careful not to draw conclusions beyond the limits of their study, and acknowledge other factors which may influence the merozoite shape, such as internal structural constraints and the energy of invasion following successful alignment.
We thank the reviewer for a thorough reading of our manuscript and the very positive judgement.
Regarding …
Author Response
Reviewer #1 (Public Review):
[...] The manuscript is excellently written and discusses the simulation results clearly and succinctly. The resolution of the simulations is very impressive and yields unprecedented insight into the effect of merozoite shape on alignment dynamics, which has important implications for how effectively the parasite can survive and multiply. The conclusions reached by the authors are certainly justified by the simulation data. In particular, the authors are careful not to draw conclusions beyond the limits of their study, and acknowledge other factors which may influence the merozoite shape, such as internal structural constraints and the energy of invasion following successful alignment.
We thank the reviewer for a thorough reading of our manuscript and the very positive judgement.
Regarding weaknesses of the manuscript, some of the explanations of the trends observed in the simulation data could be expanded slightly, to help gain a deeper understanding of the competition between adhesion and RBC deformability underlying the alignment dynamics. These are described in more detail below.
- Line 114 and lines 120-129: The discussion here of the trends observed in Figure 1 (including why the LE shape has a larger energy compared to the OB shape despite having a smaller adhesion area) is somewhat vague and should be developed further. For example, currently there is only a video showing the egg-like shape and a second video comparing the LE shape to a spherical shape - it would be helpful to have a further video comparing the LE and OB shapes and the different RBC deformations they cause. Moreover, the explanation of the energy/mobility of each shape in terms of curvatures (e.g. the OB shape having "lower curvature at its flat side") could be made more precise. I would expect that the adhesion area depends on how close the principal curvatures of the merozoite surface are to being equal and opposite to the natural curvatures of the RBC, since this determines the bending energy associated with wrapping the merozoite and forming short bonds. This would explain why the spherical shape is most mobile (its principal curvatures are constant so there is no region where at least one is relatively small), and why alignment is most likely to occur in the dimple of the RBC where the membrane is naturally concave-outward. For a given adhesion area, the deformation energy should depend on the difference in principal curvatures in the contact region, with a larger difference causing more bending of the RBC membrane. This difference is larger for the LE shape, since one principal curvature remains large at each point on the surface, compared to the OB shape whose principal curvatures are both small on the 'flat side' where contact is most likely to occur.
We have expanded the discussion of these results to make it clearer. Furthermore, a new video was generated to visually see differences between different shapes.
- Lines 175-176: Given that the ratio A_m/A_s (adhesion area to total surface area) plays a key role in the probability of alignment, the authors should be more quantitative at this point. How does the ratio A_m/A_s (as measured directly, or indirectly e.g. by the area under the probability distributions inside the alignment region in figures 3a,b) scale with the system parameters, such as the adhesion strength and the off-rate k_off? Can it be estimated from an energy balance between RBC bending/stretching and the average adhesion energy?
A change in A_m as a function of adhesion strength can be estimated analytically for a sphere, as was done in Hillringhaus et al. Biophys. J. 117:1202, 2019. For small deformations, there is essentially a competition of bending and adhesion energies, while for strong adhesion, stretching-elasticity contribution becomes important. We have included this theoretical result into the manuscript and discuss its implications.
- Line 197-198 and Figure 4c: Why is the deformation energy associated with the OB shape much lower than all other shapes for values of k_off/k_on^{long} smaller than 2?
For k_off/k_on^{long} < 2, the magnitude of local curvature has a pronounced effect. For the OB shape, a large adhesion area is formed over the area with very low curvature, and close to the rim where the curvature is large, the adhesion strength may not be strong enough to induce membrane wrapping and deformation. For other shapes, the adhesion strength is large enough to lead to partial wrapping of the parasite by the membrane over moderate curvatures. As a result, the integrated deformation energy is significantly lower for the OB shape than for the other shapes in this regime of adhesion strengths. We have added this clarification to the manuscript.
- Alignment requires that the distance between the merozoite apex and RBC membrane is very small, and the alignment criteria necessitate examining small changes in the apex angle \theta from \pi. Can the authors comment on how sensitive are the results to the numerical discretisation used?
The discretization length does affect the tightness of the alignment criteria. In our simulations, the average discretization length of the RBC membrane is about l0=0.2 m. The half circumference length of a parasite (corresponding to angle ) is R, which is equal to about 12 l0 for R=0.75 m, such that our angle resolution with respect to the parasite size is 0.1. Therefore, we use 0.2 for the alignment criteria, which is large enough to avoid strong discretization effects. Simulations with a finer discretization are possible, but they become very expensive computationally.
Reviewer #2 (Public Review):
[...] A major strength of the results is that it investigates an unstudied problem in malarial pathogenesis. The results pertaining to adhesion strength may be informative for preventing the organism from invading red blood cells. A primary weakness is that there is too little detail provided in the methods for this reviewer to adequate assess the computational method. Secondly, the results are somewhat inconclusive. While the egg-shape performs better than certain other shapes, there is no clear final understanding why this shape is preferred over the spherical or short ellipsoidal shapes. However, this possibly provides some clues as to why a certain malarial species does actively adopt a spherical shape during red blood cell binding and invasion.
We thank the reviewer for a positive judgment of our manuscript. We have significantly expanded the methods section, so it should contain now all necessary simulation details. We agree with the reviewer that the conclusions about shape advantages/disadvantages are equivocal to some extent, but this is exactly what our simulation data show. However, from our data it is clear that the two shapes (i.e. egg-like and sphere) stand out, and they also correspond to real examples of merozoite shapes. As the reviewer points out, we do discuss some clues for the importance of parasite shape in the alignment process.
Overall, the authors achieved their aims by quantitatively assessing the affect of parasite shape and adhesion strength on cell alignment, which is a proxy for invasion. The discussion at the end of the manuscript provides an accurate evaluation of the results that puts them into the context of invasion.
While to some extent the results presented here are inconclusive, I do think that this paper achieves an important goal for its field. This is an understudied area pertinent to a major disease. This manuscript has the potential to bring questions of the biophysics of malarial invasion out to the broader community, specifically introducing these questions to biophysicists as well as microbiologists. Furthermore, the results naturally lead to new questions. If the spherical and egg shapes do not confer a strong advantage, then these specific shapes must also play a role in other processes. The authors do suggest some possibilities in the Discussion. That their remain interesting questions is a great spur for future work.
Thank you for emphasizing the importance of multidisciplinarity. We also hope that our work will ignite interest in different communities, as only a multidisciplinary effort can bring us much closer to understanding of parasite alignment and invasion, which clearly include a combination of different mechanical and biochemical processes.
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Evaluation Summary:
This manuscript studies the alignment of malaria parasites (merozoites) at the surface of red blood cells (RBCs), a key element of their reproduction cycle during the blood stage of the disease. Building on a computational model the authors developed previously, which incorporates the stochastic nature of RBC deformations and adhesive bonds between the merozoite and RBC, it is demonstrated that parasite shape plays a key role in its alignment dynamics. In particular, the authors shed new light on the egg-like shape typically observed in Plasmodium merozoites, which has important implications for how effectively the parasite can survive and multiply.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the …
Evaluation Summary:
This manuscript studies the alignment of malaria parasites (merozoites) at the surface of red blood cells (RBCs), a key element of their reproduction cycle during the blood stage of the disease. Building on a computational model the authors developed previously, which incorporates the stochastic nature of RBC deformations and adhesive bonds between the merozoite and RBC, it is demonstrated that parasite shape plays a key role in its alignment dynamics. In particular, the authors shed new light on the egg-like shape typically observed in Plasmodium merozoites, which has important implications for how effectively the parasite can survive and multiply.
(This preprint has been reviewed by eLife. We include the public reviews from the reviewers here; the authors also receive private feedback with suggested changes to the manuscript. Reviewer #1 agreed to share their name with the authors.)
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Reviewer #1 (Public Review):
This manuscript studies the invasion of red blood cells (RBCs) by malaria parasites (merozoites), a key element of their reproduction cycle during the blood stage of the disease. For successful invasion to occur, the merozoite must first align its apex almost perpendicularly to the RBC membrane. In a previous study (reference Hillringhaus et al., 2020), the authors developed a computational model that incorporates stochastic deformations of the RBC membrane and the discrete nature of the adhesive bonds between the merozoite and RBC (arising from filaments on the merozoite surface); together these effects enable partial wrapping of the membrane around the merozoite to aid alignment. This manuscript builds upon this framework to examine the influence of the parasite shape on the alignment dynamics, using five …
Reviewer #1 (Public Review):
This manuscript studies the invasion of red blood cells (RBCs) by malaria parasites (merozoites), a key element of their reproduction cycle during the blood stage of the disease. For successful invasion to occur, the merozoite must first align its apex almost perpendicularly to the RBC membrane. In a previous study (reference Hillringhaus et al., 2020), the authors developed a computational model that incorporates stochastic deformations of the RBC membrane and the discrete nature of the adhesive bonds between the merozoite and RBC (arising from filaments on the merozoite surface); together these effects enable partial wrapping of the membrane around the merozoite to aid alignment. This manuscript builds upon this framework to examine the influence of the parasite shape on the alignment dynamics, using five different reference shapes: the egg-like shape typical of Plasmodium merozoites, a sphere, and ellipsoids of varying aspect ratio. By exploring the influence of various parameters such as the bond kinetics and RBC membrane stiffness, they demonstrate that the parasite shape plays a key role in its alignment dynamics. In particular, the egg-like shape is found to be more robust to different adhesion strengths and membrane deformability: it is relatively mobile compared to the ellipsoidal shapes and, unlike a sphere, does not easily become arrested in the high-adhesion limit due to its lack of spherical symmetry.
The manuscript is excellently written and discusses the simulation results clearly and succinctly. The resolution of the simulations is very impressive and yields unprecedented insight into the effect of merozoite shape on alignment dynamics, which has important implications for how effectively the parasite can survive and multiply. The conclusions reached by the authors are certainly justified by the simulation data. In particular, the authors are careful not to draw conclusions beyond the limits of their study, and acknowledge other factors which may influence the merozoite shape, such as internal structural constraints and the energy of invasion following successful alignment.
Regarding weaknesses of the manuscript, some of the explanations of the trends observed in the simulation data could be expanded slightly, to help gain a deeper understanding of the competition between adhesion and RBC deformability underlying the alignment dynamics. These are described in more detail below.
1. Line 114 and lines 120-129: The discussion here of the trends observed in Figure 1 (including why the LE shape has a larger energy compared to the OB shape despite having a smaller adhesion area) is somewhat vague and should be developed further. For example, currently there is only a video showing the egg-like shape and a second video comparing the LE shape to a spherical shape - it would be helpful to have a further video comparing the LE and OB shapes and the different RBC deformations they cause. Moreover, the explanation of the energy/mobility of each shape in terms of curvatures (e.g. the OB shape having "lower curvature at its flat side") could be made more precise. I would expect that the adhesion area depends on how close the principal curvatures of the merozoite surface are to being equal and opposite to the natural curvatures of the RBC, since this determines the bending energy associated with wrapping the merozoite and forming short bonds. This would explain why the spherical shape is most mobile (its principal curvatures are constant so there is no region where at least one is relatively small), and why alignment is most likely to occur in the dimple of the RBC where the membrane is naturally concave-outward. For a given adhesion area, the deformation energy should depend on the difference in principal curvatures in the contact region, with a larger difference causing more bending of the RBC membrane. This difference is larger for the LE shape, since one principal curvature remains large at each point on the surface, compared to the OB shape whose principal curvatures are both small on the 'flat side' where contact is most likely to occur.
2. Lines 175-176: Given that the ratio A_m/A_s (adhesion area to total surface area) plays a key role in the probability of alignment, the authors should be more quantitative at this point. How does the ratio A_m/A_s (as measured directly, or indirectly e.g. by the area under the probability distributions inside the alignment region in figures 3a,b) scale with the system parameters, such as the adhesion strength and the off-rate k_off? Can it be estimated from an energy balance between RBC bending/stretching and the average adhesion energy?
3. Line 197-198 and Figure 4c: Why is the deformation energy associated with the OB shape much lower than all other shapes for values of k_off/k_on^{long} smaller than 2?
4. Alignment requires that the distance between the merozoite apex and RBC membrane is very small, and the alignment criteria necessitate examining small changes in the apex angle \theta from \pi. Can the authors comment on how sensitive are the results to the numerical discretisation used?
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Reviewer #2 (Public Review):
This manuscript seeks to determine the role that malarial shape plays in the ability of this parasite to infect red blood cells. The authors use computational modeling to explore the dynamics of different parasite shapes and the affect of adhesion strength in getting the malaria parasite to bind into the correct orientation for invasion into the red blood cell.
A major strength of the results is that it investigates an unstudied problem in malarial pathogenesis. The results pertaining to adhesion strength may be informative for preventing the organism from invading red blood cells. A primary weakness is that there is too little detail provided in the methods for this reviewer to adequate assess the computational method. Secondly, the results are somewhat inconclusive. While the egg-shape performs better than …
Reviewer #2 (Public Review):
This manuscript seeks to determine the role that malarial shape plays in the ability of this parasite to infect red blood cells. The authors use computational modeling to explore the dynamics of different parasite shapes and the affect of adhesion strength in getting the malaria parasite to bind into the correct orientation for invasion into the red blood cell.
A major strength of the results is that it investigates an unstudied problem in malarial pathogenesis. The results pertaining to adhesion strength may be informative for preventing the organism from invading red blood cells. A primary weakness is that there is too little detail provided in the methods for this reviewer to adequate assess the computational method. Secondly, the results are somewhat inconclusive. While the egg-shape performs better than certain other shapes, there is no clear final understanding why this shape is preferred over the spherical or short ellipsoidal shapes. However, this possibly provides some clues as to why a certain malarial species does actively adopt a spherical shape during red blood cell binding and invasion.
Overall, the authors achieved their aims by quantitatively assessing the affect of parasite shape and adhesion strength on cell alignment, which is a proxy for invasion. The discussion at the end of the manuscript provides an accurate evaluation of the results that puts them into the context of invasion.
While to some extent the results presented here are inconclusive, I do think that this paper achieves an important goal for its field. This is an understudied area pertinent to a major disease. This manuscript has the potential to bring questions of the biophysics of malarial invasion out to the broader community, specifically introducing these questions to biophysicists as well as microbiologists. Furthermore, the results naturally lead to new questions. If the spherical and egg shapes do not confer a strong advantage, then these specific shapes must also play a role in other processes. The authors do suggest some possibilities in the Discussion. That their remain interesting questions is a great spur for future work.
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