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Mechanics of diseased red blood cells in human spleen and consequences for hereditary blood disorders He Li a,1 , Lu Lu a,1 , Xuejin Li a , Pierre A. Buffet b,c , Ming Dao d,2 , George E. Karniadakis a,2 , and Subra Suresh e,2 a Division of Applied Mathematics, Brown University, Providence, RI 02912; b Facult ´ e de M ´ edecine Universit ´ e Paris Descartes, Institut National de la Transfusion Sanguine, Paris 75015, France; c Laboratory of Excellence GR-Ex “The Red Blood Cell: From Genesis to Death,” Sorbonne Paris Cit ´ e, 75015 Paris, France; d Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; and e Nanyang Technological University, 639798, Singapore Contributed by Subra Suresh, July 14, 2018 (sent for review April 17, 2018; reviewed by M. Taher A. Saif and Qiang Zhu) In red blood cell (RBC) diseases, the spleen contributes to ane- mia by clearing the damaged RBCs, but its unique ability to mechanically challenge RBCs also poses the risk of inducing other pathogenic effects. We have analyzed RBCs in hereditary sphero- cytosis (HS) and hereditary elliptocytosis (HE), two typical exam- ples of blood disorders that result in membrane protein defects in RBCs. We use a two-component protein-scale RBC model to sim- ulate the traversal of the interendothelial slit (IES) in the human spleen, a stringent biomechanical challenge on healthy and dis- eased RBCs that cannot be directly observed in vivo. In HS, our results confirm that the RBC loses surface due to weakened cohe- sion between the lipid bilayer and the cytoskeleton and reveal that surface loss may result from vesiculation of the RBC as it crosses IES. In HE, traversing IES induces sustained elongation of the RBC with impaired elasticity and fragmentation in severe disease. Our simulations thus suggest that in inherited RBC disor- ders, the spleen not only filters out pathological RBCs but also directly contributes to RBC alterations. These results provide a mechanistic rationale for different clinical outcomes documented following splenectomy in HS patients with spectrin-deficient and ankyrin-deficient RBCs and offer insights into the pathogenic role of human spleen in RBC diseases. spleen | hereditary spherocytosis | hereditary elliptocytosis | vesiculation | cell fragmentation T he spleen is the largest secondary immune organ in the human body, and it consists of two functionally distinct com- partments, the white pulp and the red pulp (1, 2). The white pulp is responsible for initiating immune reactions to blood- borne antigens, whereas the red pulp serves as a primary blood filter to sequester and remove pathogenic microorganisms as well as senescent or diseased red blood cells (RBCs) from cir- culation (3–6). RBCs traversing the red pulp move from the cords into venous sinuses, where they have to squeeze through the narrow apertures, known as interendothelial slits (IESs), which are located between the elongated endothelial cells of the sinus wall. Two distinct mechanisms lead to filtering of RBCs in the red pulp: (i) physicochemical filtration, which involves adherence of surface-altered RBCs to reticular connective tis- sue and macrophages, followed by removal of adhered RBCs through phagocytosis, and (ii) mechanical filtration, whereby the IES of the sinus wall functions as a physical barrier to pro- hibit RBCs with abnormal size, shape, and deformability from returning to general circulation. These two sequential processes constantly control the quality of circulating RBCs and prevent microcirculatory complications elsewhere in the body. Healthy RBCs have remarkable deformability and stability, which enable them to undergo repeated deformation in micro- circulation during their life span of 120 d. In blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE), however, defects in RBC membrane proteins weaken the cohesion between the lipid bilayer and the cytoskeleton (in HS) or the integrity of the cytoskeleton (in HE), thereby compromis- ing the deformability and stability of RBCs (7). In HS, defects in cytoskeletal proteins or membrane proteins that anchor the cytoskeleton to the lipid bilayer destabilize the RBC membrane, leading to membrane surface loss through release of vesicles (8, 9). Loss of membrane surface causes a decrease in the ratio of surface area-to-volume (S/V) of RBCs and promotes the for- mation of spherical RBCs. Due to their reduced deformability, spherical RBCs are removed prematurely by the spleen, result- ing in mild to severe forms of anemia, dependent on the extent of surface area loss (10). In HE, defects in the cytoskeletal proteins impair the elasticity of RBCs by disrupting the integrity of the membrane cytoskeleton (9, 11). As a result, RBCs in HE undergo irreversible elongation after large deformation and progressively transform into elliptical shape (12). In severe forms of HE, RBCs become mechanically unstable, resulting in cell fragmentation and lysis (9, 11). The ensuing ill-shaped RBCs and cell fragments are cleared from circulation by the spleen, causing hemolytic anemia. The function of spleen in sensing and clearing RBCs with alterations in their size, shape, and deformability has been eluci- dated through in vivo (13, 14), ex vivo (3–5), and in vitro (15–17) experiments and computational modeling (18–21). However, the role of IES in filtering RBCs with significant membrane protein defects, as seen in HS and HE, has not been investigated in suffi- cient detail. To address these questions, we use a two-component coarse-grained molecular dynamics (CGMD) RBC model (22) to simulate the traversal dynamics of healthy, HS, and HE RBCs Significance The interendothelial slit (IES) is the narrowest circulatory path- way in the human spleen where aged and diseased red blood cells (RBCs) are filtered. We use a two-component RBC model to probe the dynamics of healthy and diseased RBCs travers- ing IES. Our simulations reveal that the spleen not only senses and clears RBCs with abnormal shapes and deformability but also alters the geometries of RBCs that contain protein defects arising from hereditary blood disorders. The framework pre- sented here is sufficiently general to be extended to elucidate the pathophysiological roles of the spleen in other blood diseases. Author contributions: H.L., X.L., P.A.B., M.D., G.E.K., and S.S. designed research; H.L. and L.L. performed research; H.L., L.L., X.L., P.A.B., M.D., G.E.K., and S.S. analyzed data; and H.L., L.L., X.L., P.A.B., M.D., G.E.K., and S.S. wrote the paper. Reviewers: M.T.A.S., University of Illinois at Urbana–Champaign; and Q.Z., University of California, San Diego. The authors declare no conflict of interest. This open access article is distributed under Creative Commons Attribution- NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND). 1 H.L. and L.L. contributed equally to this work.y 2 To whom correspondence may be addressed. Email: [email protected], George [email protected], or [email protected].y This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. 1073/pnas.1806501115/-/DCSupplemental. Published online September 6, 2018. 9574–9579 | PNAS | September 18, 2018 | vol. 115 | no. 38 www.pnas.org/cgi/doi/10.1073/pnas.1806501115

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Page 1: Mechanics of diseased red blood cells in human …...Mechanics of diseased red blood cells in human spleen and consequences for hereditary blood disorders He Li a,1, Lu Lu , Xuejin

Mechanics of diseased red blood cells in human spleenand consequences for hereditary blood disordersHe Lia,1, Lu Lua,1, Xuejin Lia, Pierre A. Buffetb,c, Ming Daod,2, George E. Karniadakisa,2, and Subra Sureshe,2

aDivision of Applied Mathematics, Brown University, Providence, RI 02912; bFaculte de Medecine Universite Paris Descartes, Institut National de laTransfusion Sanguine, Paris 75015, France; cLaboratory of Excellence GR-Ex “The Red Blood Cell: From Genesis to Death,” Sorbonne Paris Cite, 75015 Paris,France; dDepartment of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139; and eNanyang TechnologicalUniversity, 639798, Singapore

Contributed by Subra Suresh, July 14, 2018 (sent for review April 17, 2018; reviewed by M. Taher A. Saif and Qiang Zhu)

In red blood cell (RBC) diseases, the spleen contributes to ane-mia by clearing the damaged RBCs, but its unique ability tomechanically challenge RBCs also poses the risk of inducing otherpathogenic effects. We have analyzed RBCs in hereditary sphero-cytosis (HS) and hereditary elliptocytosis (HE), two typical exam-ples of blood disorders that result in membrane protein defects inRBCs. We use a two-component protein-scale RBC model to sim-ulate the traversal of the interendothelial slit (IES) in the humanspleen, a stringent biomechanical challenge on healthy and dis-eased RBCs that cannot be directly observed in vivo. In HS, ourresults confirm that the RBC loses surface due to weakened cohe-sion between the lipid bilayer and the cytoskeleton and revealthat surface loss may result from vesiculation of the RBC as itcrosses IES. In HE, traversing IES induces sustained elongationof the RBC with impaired elasticity and fragmentation in severedisease. Our simulations thus suggest that in inherited RBC disor-ders, the spleen not only filters out pathological RBCs but alsodirectly contributes to RBC alterations. These results provide amechanistic rationale for different clinical outcomes documentedfollowing splenectomy in HS patients with spectrin-deficient andankyrin-deficient RBCs and offer insights into the pathogenic roleof human spleen in RBC diseases.

spleen | hereditary spherocytosis | hereditary elliptocytosis | vesiculation |cell fragmentation

The spleen is the largest secondary immune organ in thehuman body, and it consists of two functionally distinct com-

partments, the white pulp and the red pulp (1, 2). The whitepulp is responsible for initiating immune reactions to blood-borne antigens, whereas the red pulp serves as a primary bloodfilter to sequester and remove pathogenic microorganisms aswell as senescent or diseased red blood cells (RBCs) from cir-culation (3–6). RBCs traversing the red pulp move from thecords into venous sinuses, where they have to squeeze throughthe narrow apertures, known as interendothelial slits (IESs),which are located between the elongated endothelial cells of thesinus wall. Two distinct mechanisms lead to filtering of RBCsin the red pulp: (i) physicochemical filtration, which involvesadherence of surface-altered RBCs to reticular connective tis-sue and macrophages, followed by removal of adhered RBCsthrough phagocytosis, and (ii) mechanical filtration, whereby theIES of the sinus wall functions as a physical barrier to pro-hibit RBCs with abnormal size, shape, and deformability fromreturning to general circulation. These two sequential processesconstantly control the quality of circulating RBCs and preventmicrocirculatory complications elsewhere in the body.

Healthy RBCs have remarkable deformability and stability,which enable them to undergo repeated deformation in micro-circulation during their life span of ∼120 d. In blood disordersof hereditary spherocytosis (HS) and hereditary elliptocytosis(HE), however, defects in RBC membrane proteins weaken thecohesion between the lipid bilayer and the cytoskeleton (in HS)or the integrity of the cytoskeleton (in HE), thereby compromis-ing the deformability and stability of RBCs (7). In HS, defects

in cytoskeletal proteins or membrane proteins that anchor thecytoskeleton to the lipid bilayer destabilize the RBC membrane,leading to membrane surface loss through release of vesicles (8,9). Loss of membrane surface causes a decrease in the ratio ofsurface area-to-volume (S/V) of RBCs and promotes the for-mation of spherical RBCs. Due to their reduced deformability,spherical RBCs are removed prematurely by the spleen, result-ing in mild to severe forms of anemia, dependent on the extent ofsurface area loss (10). In HE, defects in the cytoskeletal proteinsimpair the elasticity of RBCs by disrupting the integrity of themembrane cytoskeleton (9, 11). As a result, RBCs in HE undergoirreversible elongation after large deformation and progressivelytransform into elliptical shape (12). In severe forms of HE, RBCsbecome mechanically unstable, resulting in cell fragmentationand lysis (9, 11). The ensuing ill-shaped RBCs and cell fragmentsare cleared from circulation by the spleen, causing hemolyticanemia.

The function of spleen in sensing and clearing RBCs withalterations in their size, shape, and deformability has been eluci-dated through in vivo (13, 14), ex vivo (3–5), and in vitro (15–17)experiments and computational modeling (18–21). However, therole of IES in filtering RBCs with significant membrane proteindefects, as seen in HS and HE, has not been investigated in suffi-cient detail. To address these questions, we use a two-componentcoarse-grained molecular dynamics (CGMD) RBC model (22)to simulate the traversal dynamics of healthy, HS, and HE RBCs

Significance

The interendothelial slit (IES) is the narrowest circulatory path-way in the human spleen where aged and diseased red bloodcells (RBCs) are filtered. We use a two-component RBC modelto probe the dynamics of healthy and diseased RBCs travers-ing IES. Our simulations reveal that the spleen not only sensesand clears RBCs with abnormal shapes and deformability butalso alters the geometries of RBCs that contain protein defectsarising from hereditary blood disorders. The framework pre-sented here is sufficiently general to be extended to elucidatethe pathophysiological roles of the spleen in other blooddiseases.

Author contributions: H.L., X.L., P.A.B., M.D., G.E.K., and S.S. designed research; H.L. andL.L. performed research; H.L., L.L., X.L., P.A.B., M.D., G.E.K., and S.S. analyzed data; andH.L., L.L., X.L., P.A.B., M.D., G.E.K., and S.S. wrote the paper.

Reviewers: M.T.A.S., University of Illinois at Urbana–Champaign; and Q.Z., University ofCalifornia, San Diego.

The authors declare no conflict of interest.

This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND).1 H.L. and L.L. contributed equally to this work.y2 To whom correspondence may be addressed. Email: [email protected], [email protected], or [email protected]

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1806501115/-/DCSupplemental.

Published online September 6, 2018.

9574–9579 | PNAS | September 18, 2018 | vol. 115 | no. 38 www.pnas.org/cgi/doi/10.1073/pnas.1806501115

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through IES. In particular, we introduce specific transmembraneprotein defects into the RBC model and correlate the molecularbasis of the diseases to different clinical expressions of RBCs inHS and HE.

ResultsIES Model and Two-Component RBC Model. To capture the geom-etry of IES in the human spleen, we construct a model thatcomprises four solid elements, as illustrated in Fig. 1. The twovertical bars represent annular fibers with a width of 1 µm,whereas the two horizontal bars represent endothelial cells. Thethickness of the slit wall is 1.89 µm, and the width and heightof the slit are 4 µm and 1.2 µm, respectively, based on theexperimentally documented slit geometry (19).

We use the computer code OpenRBC (22) to model healthyand diseased RBCs. As shown in Fig. 1, the lipid bilayer andthe cytoskeleton as well as transmembrane proteins are explic-itly represented in the RBC model. This allows simulations ofRBC vesiculation and of cell morphological changes induced byprotein defects in blood disorders. Further details of the RBCmodel can be found in SI Appendix.

Pressure Gradients and S/V Ratio Determine the Passage of RBCsthrough IES. Over the life span of about 120 d, the cytoskeleton ofthe RBC stiffens and its membrane components undergo degra-dation, resulting in loss of surface area through release of vesicles(23–25). Senescent RBCs with reduced surface area become lessdeformable and thus are amenable to sequestration and removalin the spleen. In this section, we simulate healthy RBCs withreduced surface area traversing the splenic IES. Pressure gra-dients of 3, 5, 8, 10, 15, and 20 Paµm−1 are applied to drive theRBC through IES. These pressure gradients fall within the rangefound in in vitro experiments (17)—that is, 1 to 30 Paµm−1. Suchvalues were sufficient to reproduce the physiological dynamics ofRBCs transiting through IES in rat spleen (14). First, we modelan RBC with a surface area of 140 µm2 and volume of 90 µm3.Our simulation results show that when driven by a pressure gra-dient of 3 Paµm−1, the RBC is retained by IES (Fig. 2 A andB). When the pressure gradients are equal to or larger than5 Paµm−1, RBCs are able to pass through IES. This critical pres-sure gradient is on the same order of magnitude as the pressuregradient of ∼1 Paµm−1, which was sufficient to drive RBCs ofall sizes found in blood through the slits in microsphere experi-ments and ex vivo perfusion of human spleen (5, 15). The originsof the difference between the critical pressure gradient inferredfrom this work and the values reported from previous studies arediscussed in detail in SI Appendix.

Fig. 2 E–H illustrate a sequence of shape changes of theRBC (surface area of 140 µm2 and volume of 90 µm3) dur-ing its deformation through IES. When the RBC moves intothe slit (Fig. 2F), the portion inside the slit is being squeezed,

Fig. 1. Simulating RBC passage through IES. The membrane of the RBC isexplicitly represented by CG particles. A: actin junctions; B: spectrin particles;C: glycophorin particles; D: band-3 particles; E: lipid particles. The width andheight of the simulated slit are 4 µm and 1.2 µm, respectively. The width ofthe vertical bars is 1 µm, and the thickness of the slit wall is 1.89 µm.

Fig. 2. (A and B) An RBC with surface area of 140 µm2 and volume of90 µm3 is retained by IES under a pressure gradient of 3 Paµm−1 becauseof an insufficient driving force. (C and D) An RBC with surface area of110 µm2 and volume of 90 µm3 is retained by IES under a pressure gradientof 8 Paµm−1 due to reduced surface area. (E–H) Four sequential snapshotsof the RBC with surface area of 140 µm2 and volume of 90 µm3 passagethrough IES under a pressure gradient of 20 Paµm−1 (see Movie S1). Onlyone half of the RBC is displayed for clarity.

whereas the rest of the RBC membrane is expanded to accom-modate the excluded volume, thus forming a dumbbell shape.As the RBC moves toward the downstream side of IES, thedownstream bulge expands, while the upstream bulge shrinks.Subsequently, the cell membrane in the slit infolds toward thecell body and creates a concave region, as shown in Fig. 2G.After crossing the IES, the deformed RBC gradually spreadsout the inward-folded membrane, turning to a bullet shape (Fig.2H). The dynamics of the RBC model passage through IES areconsistent with the in vivo microscopic observations of the tran-silluminated rat spleen (14) and the in vitro microfluidic study ofhuman RBCs passage through IES-like slits (17). When drivenby increased pressure gradients, the RBC dynamics are similarexcept that the higher pressure gradients lead to faster RBCtraversal.

Next we show results for cases where the pressure gradient is5 Paµm−1 and the surface area of RBCs is reduced from 140 µm2

to 100 µm2 in decrements of 10 µm2. For the surface areasof 130 µm2 and 120 µm2, RBCs are still able to pass throughIES. However, in the case of the surface area of 110 µm2,representing about 21% surface area loss, the simulated RBCis retained by IES (Fig. 2 C and D). This result is consistentwith prior ex vivo experimental observations that RBCs withmore than 18% surface area loss were mostly entrapped in thespleen (5). This finding is also validated by an analytical model(19, 26) that defines the relationship between the critical sur-face area and volume for healthy RBCs, beyond which traversalthrough IES is predicated to be compromised. Given the geom-etry of the slit, the minimum surface area (A), below which theRBCs with fixed volume (V ) are retained by the slit, is givenby (19, 26)

A=4{2π

[f −1(V )

]2 −πf −1(V )g1(V )}

+2πLsg2(V )

{Ds

2+

Ls

2− Ls sin[g2(V )]

2g2(V )

},

[1]

where V =2[ 43πR3 − 1

3πh2(3R− h)]+ 2πAcyc . All other sym-

bols are defined in SI Appendix. This model predicts a criticalsurface area of 113.1 µm2 for the RBC volume of 90 µm3,which validates the critical area obtained from our simulations.Then, we increase the pressure gradients to 8, 10, 15, and20 Paµm−1, respectively, and we find that RBCs with surfaceareas of 110 µm2 and 100 µm2 still cannot pass through IES whendriven by these increased pressure gradients.

Traversing IES Causes Intrasplenic Vesiculation of RBCs in HS. InHS, defects occur in the RBC membrane proteins, such asankyrin, protein 4.2, band-3, and spectrin (8, 10). These protein

Li et al. PNAS | September 18, 2018 | vol. 115 | no. 38 | 9575

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deficiencies alter the RBC membrane in two distinct ways(8). In RBCs with deficiencies in the band-3 or protein 4.2,the vertical connections between the spectrin filaments andthe lipid bilayer are diminished, whereas the spectrin con-tent is normal (Fig. 3B). On the other hand, spectrin-deficientor ankyrin-deficient RBCs are characterized by depleted spec-trin content and reduced numbers of actin junction complexes,while the overall structure of the membrane cytoskeleton ispreserved (Fig. 3C). These alterations in the RBC membraneweaken the vertical linkages between the cytoskeleton andthe lipid bilayer, causing surface area loss through release ofvesicles (8, 10). HS RBCs with reduced surface area trans-form progressively from a biconcave shape to a near-sphericalshape. The concomitant decrease in cell deformability leads toRBC retention and premature removal by the spleen (5, 27).Although the genetic basis and clinical consequences of HSare known, the mechanics of membrane loss has hitherto notbeen explored in detail. In this section, we simulate band-3–deficient and spectrin-deficient RBCs traveling through IES.Varying degrees of protein deficiency are examined for thesetwo types of HS RBCs. The deformability of the HS RBCs fol-lowing reduction in surface area is evaluated by stretching theRBCs, similar to the manner in which RBC deformation wasinduced in optical tweezers experiments (28, 29). A deforma-bility index (DI) is computed based on the deformation of thestretched RBC. Details of the calculations of DI are given in SIAppendix.

We first simulate the band-3–deficient RBCs by reducingthe connectivity between the band-3 proteins and spectrin fil-aments (vertical connectivity) in the RBC model. The verticalconnectivity is reduced from 100% to 0% in decrements of

Fig. 3. (A) Cytoskeleton in a healthy RBC model. (B) In the band-3–deficientHS RBC model, the band-3 sites are randomly removed (highlighted byred dotted circles) to represent the effect of band-3 deficiency. (C) In thespectrin-deficient HS RBC model, the density of spectrin network is reducedto represent the effect of spectrin deficiency. (D–I) Six sequential snapshots(top views) of an HS RBC with a vertical connectivity of 60% passage throughIES under a pressure gradient of 10 Paµm−1(see Movie S2). Reduced verticalconnectivity leads to the detachment of the lipid bilayer from the cytoskele-ton and subsequent RBC vesiculation. The lipid CG particles (red particles)are plotted at a smaller size to visualize the cytoskeleton below (greenparticles).

20%, representing elevated degrees of band-3 deficiency. Thesurface area and volume of the simulated RBCs are 140 µm2

and 90 µm3, respectively. Fig. 3 D–I show a sequence of shapechanges of an HS RBC with a vertical connectivity of 60%as it passes through an IES (top views). Due to weakenedcohesion between the lipid bilayer and the cytoskeleton, thelipid bilayer detaches from the cytoskeleton when the RBC tra-verses IES (Fig. 3F). One detachment separates from the RBCand forms a vesicle, whereas the other develops into a tubu-lar vesicle and passes through IES behind the RBC (Fig. 3G and H). Eventually, this tubular vesicle detaches from theRBC and reshapes into a separate spherical vesicle (Fig. 3I).Detailed discussion of this vesiculation process can be foundin SI Appendix. These simulations confirm that reduced verticalconnectivity compromises the cohesion between the cytoskele-ton and the lipid bilayer and that surface area loss of RBCs inHS occurs when they traverse the IES, thereby clearly establish-ing the connection between the spleen and shape alterations indiseased RBCs.

We also examine RBCs with various vertical connectivities.At each vertical connectivity, pressure gradients of 5, 8, 10, 15,and 20 Paµm−1 are applied. The blue curve in Fig. 4A showsthat RBCs shed more surface area as the vertical connectivityis reduced. In other words, the increased degree of band-3 defi-ciency exacerbates membrane loss of the HS RBCs. Notably, thefraction of surface area loss from the HS RBCs with a verticalconnectivity of 0% is larger than the IES retention threshold(the black dashed line in Fig. 4A) inferred from ex vivo exper-iments (5), implying that these HS RBCs do not successfullypass through IES. The corresponding DI of the band-3–deficientRBCs (the blue curve in Fig. 4B) decreases as the degree of band-3 deficiency increases. These results illustrate the correlationbetween the degree of protein deficiency and clinical expressionsof RBCs in HS.

Next, we reduce the spectrin density in the cytoskeleton bydecreasing the number of actin junction complexes in the RBCmodel (Fig. 3C) to mimic spectrin-deficient RBCs. To cap-ture the wide spectrum of clinical severity observed in HS, thespectrin density is decreased from 100% (healthy) to 40% indecrements of 20%. When the spectrin-deficient RBCs passthrough IES, the lipid bilayer in the spectrin-depleted area canbud off and develop into vesicles (8). More discussion regard-ing the vesiculation process is given in SI Appendix. Fig. 4A (redcurve) illustrates that the fractional surface area loss of spectrin-deficient RBCs increases with decreased spectrin density, inagreement with clinical evidence (8). Fig. 4B shows that reducedspectrin density leads to decreased DI of the spectrin-deficientRBCs (red curve). In particular, the values of DI are consistentwith the values experimentally measured by ektacytometry at afixed osmolality of 300 mOsmol/kg (30, 31), indicating that thetrends predicted by the present results are validated by clinicalobservations.

The surface area and volume of HS RBCs following the for-mation of vesicles are plotted in Fig. 5. The blue and red symbolsin Fig. 5 show that as the HS-related protein defects increase,the S/V ratios of HS RBCs gradually decrease toward the reten-tion threshold predicted by Eq. 1 (black solid line) as well asthe retention threshold reported by ex vivo experiments (blackdashed line) (5). This plot implies that HS RBCs with lowdegrees of protein deficiency could pass IES despite reduced sur-face area. Therefore, these RBCs undergo a gradual decrease intheir life spans, leading to mild anemia. Conversely, RBCs withhigh degrees of protein deficiency undergo rapid drops of S/Vratio after crossing IES. As a result, the expected life spans ofthese RBCs are shortened markedly, leading to severe anemia.These findings provide a mechanistic rationale for the connec-tions among molecular defects, RBC alterations, and the broadspectrum of clinical severity found in HS.

9576 | www.pnas.org/cgi/doi/10.1073/pnas.1806501115 Li et al.

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Fig. 4. (A) Fractional surface area loss of HS RBCs after passage throughIES. For the band-3–deficient RBCs, the surface area loss is increasedwith the decreased vertical connectivity. For the spectrin-deficient RBCs,the surface area loss is increased with the decreased spectrin density.The error bars are computed based on pressure gradient values of 5,8, 10, 15, and 20 Paµm−1. The black dashed line highlights the criti-cal fraction of surface area loss that determines the retention of RBCsreported by ex vivo experiment (5). (B) DI of the band-3–deficientand the spectrin-deficient RBCs at different levels of HS-related pro-tein deficiency. The brown bar graph shows DI of spectrin-deficient RBCsmeasured by osmotic gradient ektacytometry at a fixed osmolality of300 mOsmol/kg (30).

Fig. 4A shows that as the level of HS-related protein defi-ciency increases, the spectrin-deficient RBCs with dispersedcytoskeleton shed more membrane surface than the band-3–deficient RBCs whose cytoskeleton is dense. Fig. 5 also showsthat as the spectrin density decreases, the spectrin-deficientRBCs (red symbols) undergo a more rapid drop of S/V ratiothan the band-3–deficient RBCs (blue symbols) for the samedecrease in volume. These results suggest that the spectrin-deficient RBCs are more amenable to vesiculation than theband-3–deficient RBCs when traversing IES. This finding pro-vides a compelling mechanistic rationale for the clinically doc-umented observation that splenectomy prolongs the survival ofspectrin/ankyrin-deficient RBCs but not band-3–deficient RBCs(32). The distinct clinical manifestations between these two typesof HS RBCs are likely attributed to the fact that the band-3–deficient RBCs in the spleen shed surface area to the sameextent as they do through other mechanisms, such as by antibody-triggered vesiculation or trogocytosis (32), while the spectrin-deficient RBCs lose membrane surface predominantly in thespleen.

Traversing IES Causes Shape Transition and Fragmentation of RBCs inHE. In HE, defects occur in cytoskeletal proteins of RBCs, suchas α-spectrin, β-spectrin, and protein 4.1R (11). The α- and β-spectrin deficiencies, which account for nearly 95% of HE cases,disrupt the self-association of spectrin dimers, whereas the pro-tein 4.1R deficiency, responsible for ∼5% of HE cases, altersthe cohesion of the spectrin–actin–protein 4.1R junctional com-plexes (11, 33). The characteristics of RBCs in HE are increasedcell fragility and shape transition from the biconcave to theelliptical shape (9, 11). In severe forms of HE, cell fragmentshave been detected in patients’ blood smear (9). The prevail-ing hypothesis is that RBCs in HE become damaged duringtheir transit through narrow pathways in microcirculation (33,34), although little clinical evidence is available to support thishypothesis. Here, we examine RBCs displaying different degreesof HE-related protein deficiency as they travel through IESand explore how the traversal through IES contributes to thepathological alterations of RBCs in HE. We break the spectrinfilaments in the RBC model (Fig. 6 A, Inset), mimicking the dis-rupted spectrin tetramers. As the severity of HE varies accordingto the degree of the impaired cytoskeleton (33), we reduce thepercentage of the intact spectrin filaments (horizontal connectiv-ity) from 100% to 20% in decrements of 10%. At each horizontalconnectivity, pressure gradients of 5, 8, 10, 15, and 20 Paµm−1

are examined.A notable feature of HE RBCs is the elongation of RBCs

after passage through IES (Fig. 6 B–D). Although vesiculationof HE RBCs is also observed, it is less pronounced comparedwith that of HS RBCs. Here, we quantify the shape transi-tion of HE RBCs by computing the aspect ratio of cells aftertheir egress from IES. The aspect ratio is defined as LA/LT,where LA is the length of the RBC along its moving direc-tion and LT is the length of the RBC perpendicular to itsmoving direction. As shown in Fig. 6A, RBCs with decreased

Fig. 5. Prediction of splenic IES retention for healthy RBCs (no protein defi-ciency) and HS RBCs. Healthy RBCs (green color symbols) with surface areaof 140 (�), 130(H), 120 (•), 110 (N), and 100 µm2 (�) and a fixed volume of90 µm3 are examined, respectively. The surface area and volume of HS RBCsafter their passage through IES are plotted. Blue color symbols denote theband-3–deficient RBCs with vertical connectivities of 80% (H), 60% (•), 40%(×), 20% (N), and 0% (�). Red color symbols denote the spectrin-deficientRBCs with spectrin density of 80% (H), 60% (•), and 40% (×). The errorbars are computed based on pressure gradient values of 5, 8, 10, 15, and20 Paµm−1. The black solid and dashed lines highlight the RBC retentionthreshold predicted by an analytical model given by Eq. 1 (19, 26) and thethreshold reported by ex vivo experiment (5), respectively. RBCs with surfacearea and volume above these thresholds are able to cross IES; otherwise,RBCs are retained by IES.

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Fig. 6. (A) Aspect ratios of HE RBCs after passage through IES. When thehorizontal connectivity is reduced to 40% or less, HE RBCs break into frag-ments due to reduced cytoskeleton integrity. The error bars are computedbased on pressure gradient values of 5, 8, 10, 15, and 20 Paµm−1. Insetshows that in the spectrin-deficient HE RBC model, spectrin filaments arerandomly disassociated (highlighted by red dotted circles), mimicking thedisrupted spectrin tetramers. (B–D) Three sequential snapshots (top views)of an HE RBC with a horizontal connectivity of 50% crossing IES (see MovieS3). (E–G) Three sequential snapshots (top views) of an HE RBC with a hor-izontal connectivity of 20% breaking into fragments after crossing IES (seeMovie S4).

horizontal connectivity undergo further elongation during theirpassage through IES. These elongated HE RBCs cannot fullyrecover their original biconcave shape due to impaired cellelasticity, leading to the progressive shape transition to ellip-tical shape. When the horizontal connectivity is 40% or less(30% and 20% in our simulations), the model predicts thatthe HE RBCs break into cell fragments. Fig. 6 E–G illustratethree sequential snapshots of an RBC with a horizontal con-nectivity of 20% passage through IES. It is noted that theportions of RBCs protruding into the luminal sides of IESare elongated and subsequently break apart from the RBC,forming two cell fragments. These simulations provide a mech-anistic rationale for RBC fragmentation in HE and for thepresence of cell fragments in the blood smear of HE patients(9, 11).

DiscussionCirculating healthy human RBCs have a life span of ∼120 d,during which they experience gradual degradation of membranecomponents and progressive loss of surface area through releaseof vesicles (23, 24, 35). Loss of surface area leads to alterationsof the shape, size, and deformability of RBCs. Removal of agedRBCs from circulation mainly occurs in the spleen, where the lessdeformable RBCs are retained by IES and subsequently phago-cytosed by macrophages (27). Our present simulation resultsshow that the S/V ratio of RBCs is an essential determinant of

their passage through IES, confirming the function of IES infiltering senescent RBCs (1, 3). In particular, our simulationsillustrate that the critical surface area that allows RBCs witha fixed volume of 90 µm3 to successfully cross IES is between110 µm2 and 120 µm2. This finding is consistent with the valuereported from ex vivo experiments (5) and with the predictionof an analytical model (19, 26). These results demonstrate thecapability of our model in quantitatively assessing RBC filtrationfunction in the spleen.

Altered RBCs in HS are characterized by spherical shape andimpaired deformability, which results from the reduced surfacearea (8–10). Our simulations illustrate that HS RBCs lose surfacearea through shedding vesicles when traversing IES because ofthe weakened cohesion between cytoskeleton and lipid bilayer.Loss of surface area from HS RBCs becomes more pronouncedas the degree of inherited protein deficiency increases. Oursimulation results also demonstrate that the reduction in sur-face area compromises the deformability of RBCs, potentiallyleading to their splenic retention by IES. As shown in Fig. 5,the S/V ratios of HS RBCs after losing surface area decreasetoward the retention thresholds (black solid and dashed lines).HS RBCs with low levels of protein deficiency undergo a smalldrop of S/V ratio after passage through IES, indicating a grad-ual decrease in their life spans, whereas HS RBCs with higherprotein deficiency undergo a larger drop of S/V ratio, implyinga marked decrease in their life spans. These findings corre-late well with the severity of anemia and earlier occurrenceof chronic complications induced by hemolysis in patients withsevere forms of HS. In addition, our simulation results sug-gest that the spectrin-deficient RBCs are more amenable tovesiculation than the band-3–deficient RBCs when traversingIES. This result provides a possible explanation of the distinctclinical outcomes of splenectomy in HS patients with differentpathogenesis (32).

The present simulations do not account for the effect of a puta-tively impaired splenic RBC filtration function in HS patients(15, 36). Therefore, the prediction of RBC retention in Figs.4A and 5 may overestimate the function of IES in retaining thealtered RBCs in HS. In addition, the reduced surface area in HSRBCs can provoke a transient dehydration, leading to a decreasein cell volume and thus an attendant increase in the S/V ratio (5,37). As a result, a greater than expected proportion of HS RBCsmay escape splenic retention and return to circulation. Althoughour present study strongly suggests that the surface area lossfrom HS RBCs occurs when they cross IES in the spleen, thispathogenic process may begin even earlier when reticulocytes(young RBCs) exit from the bone marrow, a process not devoidof mechanical constraints (37). These two mechanisms of sur-face area loss are not mutually exclusive, as reticulocytes exit thebone marrow only once but cross IES in the spleen many timesduring their life span.

The major molecular basis of HE is the α- or β-spectrin defi-ciency, which disrupts the self-association of spectrin dimer intotetramers or oligomers, leading to a weak and fragile mem-brane cytoskeleton (9, 11). Elongated cell shape and decreasedmembrane stability are the clinical features of RBCs in HE (12).Our simulations demonstrate that due to impaired cytoskele-ton, HE RBCs are elongated after traversing IES, contribut-ing to their shape transition to ellipsoids. When the sever-ity of HE-related protein deficiency is high, RBCs break intofragments during their passage through IES. These findingsclarify the relationship among the genetics, degree of proteindeficiency in cytoskeleton, and clinical expressions of RBCsin HE.

Taken together, our simulations provide unique insights intothe dual pathophysiological function of the spleen. The spleennot only assesses the mechanical fitness of the healthy and dis-eased RBCs in circulation but also contributes directly to the

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alterations of diseased RBCs. Our results also elucidate theconnections among the molecular basis of inherited RBC disor-ders, the different clinical manifestations of RBCs, the resultingsymptoms, and the clinical outcomes of splenectomy. The com-putational framework presented in the current work thus offerspossibilities to study the complex role of the spleen in thepathogenesis of RBC disorders.

ACKNOWLEDGMENTS. H.L. and X.L. thank Dr. Zhangli Peng for settingup dissipative particle dynamics simulations for model comparison. Thework was supported by National Institutes of Health Grants U01HL114476and U01HL116323. This research used resources of the Argonne Leader-ship Computing Facility under Contract DE-AC02-06CH11357 and resourcesof the Oak Ridge Leadership Computing Facility under Contract DE-AC05-00OR22725. S.S. acknowledges support from the Distinguished UniversityProfessorship at Nanyang Technological University.

1. Mebius RE, Kraal G (2005) Structure and function of the spleen. Nat Rev Immunol5:606–616.

2. Petroianu A (2011) The Spleen (Bentham Science Publishers, Hilversum, TheNetherlands).

3. Buffet PA, et al. (2006) Ex vivo perfusion of human spleens maintains clearing andprocessing functions. Blood 107:3745–3752.

4. Safeukui I, et al. (2008) Retention of plasmodium falciparum ring-infected erythro-cytes in the slow, open microcirculation of the human spleen. Blood 112:2520–2528.

5. Safeukui I, et al. (2012) Quantitative assessment of sensing and sequestration ofspherocytic erythrocytes by the human spleen. Blood 120:424–430.

6. Ndour PA, et al. (2015) Role of the Spleen in Human Malaria (Springer, New York).7. Narla J, Mohandas N (2017) Red cell membrane disorders. Int J Lab Hematol 39:47–52.8. Eber S, Lux SE (2004) Hereditary spherocytosis—Defects in proteins that connect the

membrane skeleton to the lipid bilayer. Semin Hematol 41:118–141.9. Da Costa L, Galimand J, Fenneteau O, Mohandas N (2013) Hereditary spherocytosis,

elliptocytosis, and other red cell membrane disorders. Blood Rev 27:167–178.10. Perrotta S, Gallagher PG, Mohandas N (2008) Hereditary spherocytosis. Lancet

372:1411–1426.11. Gallagher PG (2004) Hereditary elliptocytosis: Spectrin and protein 4.1R. Semin

Hematol 41:142–164.12. Diez-Silva M, Dao M, Han J, Lim CT, Suresh S (2010) Shape and biomechanical

characteristics of human red blood cells in health and disease. MRS Bull 35:382–388.13. Groom A, Schmidt E, MacDonald I (1991) Microcirculatory pathways and blood flow

in spleen: New insights from washout kinetics, corrosion casts, and quantitativeintravital videomicroscopy. Scanning Microsc 5:159–173.

14. MacDonald I, Ragan D, Schmidt E, Groom A (1987) Kinetics of red blood cell passagethrough interendothelial slits into venous sinuses in rat spleen, analyzed by in vivomicroscopy. Microvasc Res 33:118–134.

15. Deplaine G, et al. (2011) The sensing of poorly deformable red blood cells by thehuman spleen can be mimicked in vitro. Blood 117:e88–e95.

16. Picot J, et al. (2015) A biomimetic microfluidic chip to study the circulation andmechanical retention of red blood cells in the spleen. Am J Hematol 90:339–345.

17. Gambhire P, et al. (2017) High aspect ratio sub-micrometer channels using wet etch-ing: Application to the dynamics of red blood cell transiting through biomimeticsplenic slits. Small 13:1700967.

18. Freund JB (2013) The flow of red blood cells through a narrow spleen-like slit. PhysFluids 25:110807.

19. Pivkin IV, et al. (2016) Biomechanics of red blood cells in human spleen andconsequences for physiology and disease. Proc Natl Acad Sci USA 113:7804–7809.

20. Salehyar S, Zhu Q (2016) Deformation and internal stress in a red blood cell as it isdriven through a slit by an incoming flow. Soft Matter 12:3156–3164.

21. Zhu Q, Salehyar S, Cabrales P, Asaro RJ (2017) Prospects for human erythrocyteskeleton-bilayer dissociation during splenic flow. Biophysical J 113:900–912.

22. Tang YH, et al. (2017) OpenRBC: A fast simulator of red blood cells at proteinresolution. Biophys J 112:2030–2037.

23. Sutera S, et al. (1985) Age-related changes in deformability of human erythrocytes.Blood 65:275–282.

24. Waugh RE, et al. (1992) Rheologic properties of senescent erythrocytes: Loss ofsurface area and volume with red blood cell age. Blood 79:1351–1358.

25. Kiefer CR, Snyder LM (2000) Oxidation and erythrocyte senescence. Curr OpinHematol 7:113–116.

26. Pivkin IV, et al. (2017) Correction for Pivkin, et al., Biomechanics of red blood cells inhuman spleen and consequences for physiology and disease. Proc Natl Acad Sci USA114:E4521–E4521.

27. de Back DZ, Kostova EB, van Kraaij M, van den Berg TK, Van Bruggen R (2014) Ofmacrophages and red blood cells; a complex love story. Front Physiol 5:79.

28. Dao M, Lim CT, Suresh S (2003) Mechanics of the human red blood cell deformed byoptical tweezers. J Mech Phys Sol 51:2259–2280.

29. Suresh S, et al. (2005) Connections between single-cell biomechanics and humandisease states: Gastrointestinal cancer and malaria. Acta Biomater 23:3–15.

30. Suresh S (2006) Mechanical response of human red blood cells in health and disease:Some structure-property-function relationships. J Mater Res 21:1871–1877.

31. Walensky L (2003) Disorders of the Red Blood Cell Membrane (Lippincott Williams &Wilkins, Philadelphia), pp 1709–1858.

32. Reliene R, et al. (2002) Splenectomy prolongs in vivo survival of erythrocytes dif-ferently in spectrin/ankyrin-and band 3–deficient hereditary spherocytosis. Blood100:2208–2215.

33. An X, Mohandas N (2008) Disorders of red cell membrane. Br J Haematol 141:367–375.34. Mohandas N, Gallagher PG (2008) Red cell membrane: Past, present, and future.

Blood 112:3939–3948.35. Gifford SC, Derganc J, Shevkoplyas SS, Yoshida T, Bitensky MW (2006) A detailed study

of time-dependent changes in human red blood cells: From reticulocyte maturationto erythrocyte senescence. Br J Haematol 135:395–404.

36. Buchanan GR, Holtkamp CA (1987) Pocked erythrocyte counts in patients withhereditary spherocytosis before and after splenectomy. Am J Hematol 25:253–257.

37. Da Costa L, et al. (2001) Temporal differences in membrane loss lead to distinct retic-ulocyte features in hereditary spherocytosis and in immune hemolytic anemia. Blood98:2894–2899.

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