MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease

<div><p>Healthy red blood cells (RBCs) have remarkable deformability, squeezing through narrow capillaries as small as 3 microns in diameter without any damage. However, in many hematological disorders the spectrin network and lipid bilayer of diseased RBCs may be significantly altered, leading to impaired functionality including loss of deformability. We employ a two-component whole-cell multiscale model to quantify the biomechanical characteristics of the healthy and diseased RBCs, including <i>Plasmodium falciparum</i>-infected RBCs (<i>Pf</i>-RBCs) and defective RBCs in hereditary disorders, such as spherocytosis and elliptocytosis. In particular, we develop a <i>two-step multiscale framework</i> based on coarse-grained molecular dynamics (CGMD) and dissipative particle dynamics (DPD) to predict the static and dynamic responses of RBCs subject to tensile forcing, using experimental information only on the structural defects in the lipid bilayer, cytoskeleton, and their interaction. We first employ CGMD on a small RBC patch to compute the shear modulus, bending stiffness, and network parameters, which are subsequently used as input to a whole-cell DPD model to predict the RBC shape and corresponding stress field. For <i>Pf</i>-RBCs at trophozoite and schizont stages, the presence of cytoadherent knobs elevates the shear response in the lipid bilayer and stiffens the RBC membrane. For RBCs in spherocytosis and elliptocytosis, the bilayer-cytoskeleton interaction is weakened, resulting in substantial increase of the tensile stress in the lipid bilayer. Furthermore, we investigate the transient behavior of stretching deformation and shape relaxation of the normal and defective RBCs. Different from the normal RBCs possessing high elasticity, our simulations reveal that the defective RBCs respond irreversibly, <i>i.e.</i>, they lose their ability to recover the normal biconcave shape in successive loading cycles of stretching and relaxation. Our findings provide fundamental insights into the microstructure and biomechanics of RBCs, and demonstrate that the <i>two-step multiscale framework</i> presented here can be used effectively for <i>in silico</i> studies of hematological disorders based on first principles and patient-specific experimental input at the protein level.</p></div

Two-step multiscale framework for RBC modeling.

<p>The experimental information about the structural defects of the lipid bilayler, the cytoskeleton and their coupling via the transmembrane proteins is collected and considered as input to two-component composite CGMD model. The CGMD is then employed on a small RBC patch to compute the shear modulus (<i>μ</i>₀), bending stiffness (<i>k</i>_<i>c</i>), and network parameters (<i>k</i>_<i>bs</i>), which are subsequently used as input to a whole-cell DPD model to predict the RBC shape and corresponding stress field. ‡ A schematic diagram of nanoscale knob on the membrane surface of a <i>Pf</i>-RBC.</p

Stretching responses of RBCs at stretching force F_<i>s</i> = 140 pN as a function of (A) tangential friction coefficient, <i>f</i>_<i>bs</i>, and (B) elastic interaction coefficient, <i>k</i>_<i>bs</i>.

<p>In this figure, <i>f</i>_<i>bs</i> is ranged from 0.00194 to 0.194 pN⋅<i>μ</i>m⁻¹s⁻¹, and <i>k</i>_<i>bs</i> from 0.46 to 46 pN/<i>μ</i>m.</p

Shear moduli of RBCs at different pathological conditions.

<p>Shear moduli of RBCs at different pathological conditions.</p

(A) Stretching response and (B-C) corresponding stress field of H-RBCs and defective RBCs under different stretching force.

<p>The black squares show experimental results from Ref. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005173#pcbi.1005173.ref002" target="_blank">2</a>]. The stress contours of (<b>B</b>) H-RBCs and (<b>C</b>) defective RBCs at stretching force F_<i>s</i> = 0, 80, and 160 pN are shown.</p

Variation of axial (<i>D</i>_A) and transverse (<i>D</i>_T) diameters of (A) H-RBCs and (B) defective RBCs at stretching force F_<i>s</i> = 110 pN under stretching-relaxation cycles.

<p>Snapshots of RBC shape at time <i>t</i> = 0, 0.18, 0.46, 0.78, and 2.30 s are shown.</p

Shape deformation and corresponding stress field of H-RBCs, T-RBCs and S-RBCs.

<p>(<b>A</b>) The axial (<i>D</i>_A) and transverse (<i>D</i>_T) diameters of H-RBC, T-RBC, and S-RBC at stretching force F_<i>s</i> = 110 pN. For comparison, the stretching responses in experiments from Ref. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005173#pcbi.1005173.ref002" target="_blank">2</a>] and one-component whole-cell model from Ref. [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005173#pcbi.1005173.ref024" target="_blank">24</a>] are shown. (<b>B</b>) Functional dependence of EI values of T-RBCs and S-RBCs on knob density at stretching force F_<i>s</i> = 110 pN. (<b>C</b>) Corresponding stress contours of stretched H-RBC, T-RBC (<i>ρ</i>_knob,DPD≈ 7 knobs/<i>μ</i>m²), and S-RBC (<i>ρ</i>_knob,DPD≈ 12 knobs/<i>μ</i>m²).</p

Schematic representation of the two-component composite CGMD model (A & C) and whole-cell DPD model (B & D) of H-RBCs and <i>Pf</i>-RBCs.

<p>For the composite CGMD model, the red, blue, and grey particles represent clusters of lipid molecules, actin junctions, and actin filaments of cytoskeleton, respectively; the black and yellow particles signify band-3 complexes, of which one third (yellow ones) are connected to the spectrin network; the green patches represent the rigid knobs in the <i>Pf</i>-RBC membrane; the purple particles refer to the spectrin octamers. For the whole-cell DPD model, the lipid bilayer and cytoskeleton are rendered in red and grey triangular networks, respectively. Only half of the triangular network of the lipid bilayer is shown for clarity. The rigid knobs in lipid bilayer of the <i>Pf</i>-RBC is rendered in green, while the enhanced spectrin network of T-RBC and deficient spectrin network of S-RBC are highlighted in purple bonds and visible holes in the triangular network of the cytoskeleton. The knob density in the whole-cell DPD model is set to be lower than that in the composite CGMD model due to different levels of coarse-graining applied to these two-component models. In the whole-cell DPD model, the average size of a knob (<i>A</i>_knob,DPD) is around 0.04 <i>μ</i>m² and 0.036 <i>μ</i>m² for T-RBC and S-RBC, respectively, which is around 2–5 times bigger than that (<i>A</i>_knob,CGMD) used in the composite CGMD model. Thus, <i>ρ</i>_knob,DPD ≈ (0.2–0.5)<i>ρ</i>_knob,CGMD.</p

Assembly of Lock-and-Key Colloids Mediated by Polymeric Depletant

Polymer-mediated lock-and-key assembly via depletion attraction is purely a shape-recognition process without any molecular bonding. Since the depletion attraction relates to osmotic pressure and excluded volume, the binding tendency in a dispersion of lock-and-key colloids can be controlled by adjusting the characteristics of polymeric depletants. In this work, dissipative particle dynamics accounting for explicit solvents, polymers, and multiple lock–key pairs are performed to investigate the influences of the polymer concentration, chain length, solvent quality, and chain stiffness. As the polymer concentration associated with osmotic pressure is increased, the binding free energy (<i>E</i>_b) between a lock–key pair rises linearly and the binding fraction (θ_LK) in the dispersion grows sigmoidally. Moreover, the increases in the chain length, solvent quality, and chain stiffness lead to the expansion of the polymer size associated with excluded volume and thus both <i>E</i>_b and θ_LK rise accordingly. However, <i>E</i>_b and θ_LK grow to be insensitive to the chain length for long enough polymer coils but still can be enhanced if the polymer becomes rod-like. As the solvent quality is varied, θ_LK can be dramatically altered, although the radius of gyration of polymers is slightly changed

Electrocatalytic Zinc Composites as the Efficient Counter Electrodes of Dye-Sensitized Solar Cells: Study on the Electrochemical Performances and Density Functional Theory Calculations

Highly efficient zinc compounds (Zn₃N₂, ZnO, ZnS, and ZnSe) have been investigated as low-cost electrocatalysts for the counter electrodes (CE) of dye-sensitized solar cells (DSSCs). Among them, Zn₃N₂ and ZnSe are introduced for the first time in DSSCs. The zinc compounds were separately mixed with a conducting binder, poly­(3,4-ethylene-dioxythiophene):poly­(styrenesulfonate) (PEDOT:PSS), and thereby four composite films of Zn₃N₂/PEDOT:PSS, ZnO/PEDOT:PSS, ZnS/PEDOT:PSS, and ZnSe/PEDOT:PSS were coated on the tin-doped indium oxide (ITO) substrates through a simple drop-coating process. In the composite film, nanoparticles of the zinc compound form active sites for the electrocatalytic reduction of triiodide ions, and PEDOT:PSS provides a continuous conductive matrix for fast electron transfer. By varying the weight percentage (5–20 wt %) of a zinc compound with respect to the weight of the PEDOT:PSS, the optimized concentration of a zinc compound was found to be 10 wt % in all four cases, based on the photovoltaic performances of the corresponding DSSCs. At this concentration (10 wt %), the composites films with Zn₃N₂ (Zn₃N₂-10), ZnO (ZnO-10), ZnS (ZnS-10), and ZnSe (ZnSe-10) rendered, for their DSSCs, power conversion efficiencies (η) of 8.73%, 7.54%, 7.40%, and 8.13%, respectively. The difference in the power conversion efficiency is explained based on the electrocatalytic abilities of those composite films as determined by cyclic voltammetry (CV), Tafel polarization plots, and electrochemical impedance spectroscopy (EIS) techniques. The energy band gaps of the zinc compounds, obtained by density functional theory (DFT) calculations, were used to explain the electrocatalytic behaviors of the compounds. Among all the zinc-based composites, the one with Zn₃N₂-10 showed the best electrocatalytic ability and thereby rendered for its DSSC the highest η of 8.73%, which is even higher than that of the cell with the traditional Pt CE (8.50%). Therefore, Zn₃N₂ can be considered as a promising inexpensive electrocatalyst to replace the rare and expensive Pt