Encapsulation of Concentrated Hemoglobin Solution in Phospholipid Vesicles Retards the Reaction with NO, but Not CO, by Intracellular Diffusion Barrier*

One physiological significance of the red blood cell (RBC) structure is that NO binding of Hb is retarded by encapsulation with the cell membrane. To clarify the mechanism, we analyzed Hb-vesicles (HbVs) with different intracellular Hb concentrations, [Hb]in, and different particle sizes using stopped-flow spectrophotometry. The apparent NO binding rate constant, \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(k_{\mathrm{on}}^{{^\prime}(\mathrm{NO})}\) \end{document}, of HbV at [Hb]in = 1 g/dl was 2.6 × 107 m-1 s-1, which was almost equal to kon(NO) of molecular Hb, indicating that the lipid membrane presents no obstacle for NO binding. With increasing [Hb]in to 35 g/dl, \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(k_{\mathrm{on}}^{{^\prime}(\mathrm{NO})}\) \end{document} decreased to 0.9 × 107 m-1 s-1, which was further decreased to 0.5 × 107 m-1 s-1 with enlarging particle diameter from 265 to 452 nm. For CO binding, which is intrinsically much slower than NO binding, \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(k_{\mathrm{on}}^{{^\prime}(\mathrm{CO})}\) \end{document} did not change greatly with [Hb]in and the particle diameter. Results obtained using diffusion simulations coupled with elementary binding reactions concur with these tendencies and clarify that NO is trapped rapidly by Hb from the interior surface region to the core of HbV at a high [Hb]in, retarding NO diffusion toward the core of HbV. In contrast, slow CO binding allows time for further CO-diffusion to the core. Simulations extrapolated to larger particles (8 μm) showing retardation even for CO binding. The obtained \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(k_{\mathrm{on}}^{{^\prime}(\mathrm{NO})}\) \end{document} and \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(k_{\mathrm{on}}^{{^\prime}(\mathrm{NO})}\) \end{document} yield values similar to those reported for RBCs. In summary, the intracellular, not extracellular, diffusion barrier is predominant due to the rapid NO binding that induces a rapid sink of NO from the interior surface to the core, retarding further NO diffusion and binding.

One physiological significance of the red blood cell (RBC) structure is that NO binding of Hb is retarded by encapsulation with the cell membrane. To clarify the mechanism, we analyzed Hb-vesicles (HbVs) with different intracellular Hb concentrations, [Hb] in , and different particle sizes using stopped-flow spectrophotometry. The apparent NO binding rate constant, k on (NO) , of HbV at [Hb] in ‫؍‬ 1 g/dl was 2.6 ؋ 10 7 M ؊1 s ؊1 , which was almost equal to k on (NO) of molecular Hb, indicating that the lipid membrane presents no obstacle for NO binding. With increasing [Hb] in to 35 g/dl, k on (NO) decreased to 0.9 ؋ 10 7 M ؊1 s ؊1 , which was further decreased to 0.5 ؋ 10 7 M ؊1 s ؊1 with enlarging particle diameter from 265 to 452 nm. For CO binding, which is intrinsically much slower than NO binding, k on (CO) did not change greatly with [Hb] in and the particle diameter. Results obtained using diffusion simulations coupled with elementary binding reactions concur with these tendencies and clarify that NO is trapped rapidly by Hb from the interior surface region to the core of HbV at a high [Hb] in , retarding NO diffusion toward the core of HbV. In contrast, slow CO binding allows time for further CO-diffusion to the core. Simulations extrapolated to larger particles (8 m) showing retardation even for CO binding. The obtained k on (NO) and k on (CO) yield values similar to those reported for RBCs. In summary, the intracellular, not extracellular, diffusion barrier is predominant due to the rapid NO binding that induces a rapid sink of NO from the interior surface to the core, retarding further NO diffusion and binding.
Physicochemical analyses of O 2 uptake and release behaviors of red blood cells (RBCs) 3 have revealed that the cellular struc-ture retards all reactions in comparison with the homogeneous cell-free Hb solution (1)(2)(3)(4)(5). However, nature has selected this cellular structure through evolution. Reasons for Hb encapsulation in RBCs are as follows: (i) decreases in a high colloidal osmotic pressure of an Hb solution; (ii) prevention of removal of Hb from blood circulation through renal gloreruli; (iii) preservation of the chemical environment in cells, such as the concentrations of electrolytes (phosphates, 2,3-diphosphoglyceric acid, ATP, etc.) and many enzymes; and (iv) modulation of entrapment of endogenous gaseous messenger molecules (NO and CO) (6,7) because it has been clarified in pathological conditions with hemolysis (8) and in the development of some Hbbased oxygen carriers (HBOCs) (9 -16) that entrapment of endothelium-derived NO induces vasoconstriction, hypertension, reduced blood flow, and vascular damage. CO is also a vasorelaxation factor, especially in hepatic microcirculation (17). Entrapment of CO by a cell-free Hb solution induces constriction of sinusoidal capillaries (18). These side effects of molecular Hb imply the importance of the cellular structure of RBC.
Despite such a background in this field, the mechanism of retardation of NO binding by Hb encapsulation in RBC remains controversial (19 -21). It remains unclear whether (i) an unstirred layer is formed as an extracellular diffusion barrier surrounding the RBC (6,9); (ii) a protein-rich RBC cytoskeletal submembrane becomes a physical barrier against NO diffusion (22,23); or (iii) gas diffusion is retarded because of the viscous Hb solution in RBC (2). As chemists, it seems to us that these controversies are attributable to the complex and fragile structure of RBC and chemically unstable NO, which make it difficult to analyze the binding rate constant of NO to RBC.
Hemoglobin-vesicles (HbVs) or liposome-encapsulated Hbs have been developed as transfusion alternatives. Their efficacy as O 2 carriers is comparable with that of RBC (24 -28). It has been thought that liposomes as a molecular assembly are a fragile capsule. However, appropriate lipid composition and polyethylene glycol modification on the surface of vesicles stabilize the dispersion state (29) and enable stopped-flow measure-ments without causing hemolysis (26,30). Although stoppedflow measurement is becoming classical, it allows accurate measurement of the binding rate constant of ligands (31). HbV is a molecular assembly composed of lipids and a concentrated Hb solution (32), and its physicochemical properties can be regulated easily (33)(34)(35) to elucidate their influences on the ligand binding profiles. In this paper, we describe analyses of the influences of intracellular Hb concentration, [Hb] in , and the particle size of HbV on the apparent binding rate constants of NO and CO. Moreover, we attempted computer simulations to recreate the phenomena, clarify the underlying mechanism, and predict the ligand binding profiles of larger particles, such as RBCs.

Preparation of Hb Solution and Hb-vesicles with Various
[Hb] in -A concentrated human carbonylhemoglobin solution (40 g/dl, desalted) was obtained through purification from outdated donated blood provided by the Japanese Red Cross Society (Tokyo, Japan), as reported previously (36,37). This was diluted by 10 times with a phosphate-buffered saline (PBS) solution (pH 7.4; Wako Pure Chemical Industries Ltd., Tokyo). It was then concentrated again to 40 g/dl using an ultrafiltration (cut-off M r 10,000; Advantec, Tokyo) at 4°C. This solution was diluted to 1, 10, 20, and 35 g/dl using the same PBS solution. They were used for preparation of HbV with different [Hb] in . The viscosities of these Hb solutions were measured using a rheometer (Physica MCR 301; Anton Paar GmbH, Graz, Austria) as 0.9, 1.1, 2.1, and 10.1 centipose, respectively, at 10 s Ϫ1 and 25°C. In this experiment, we added no allosteric effector, such as an organic phosphate, because we intended to compare the Hb solution and HbV with different [Hb] in at the same O 2 affinity (P 50 , oxygen partial pressure at which Hb is half-saturated). A linear relationship exists between P 50 and NO affinity of Hb (38). In the present study, P 50 was regulated solely using Cl Ϫ and phosphate of PBS (35). The lipid bilayer comprised 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine, cholesterol, 1,5-O-dihexadecyl-N-succinyl-L-glutamate (Nippon Fine Chemical Co. Ltd., Osaka, Japan), and 1,2-distearoylsn-glycerol-3-phosphatidylethanolamine-N-polyethylene glycol 5000 (NOF Corp., Tokyo, Japan) at a molar composition of 5/5/1/0.033. It is reported that unsaturated phospholipids are susceptible to lipid peroxidation and induce Hb denaturation (39,40). Hb interacts with such a liposomal membrane and converts to metHb, leading synergistically to the heme loss and lipid peroxidation. Unsaturated fatty acid is susceptible to nitration (41). However, we use saturated phospholipids that essentially do not induce such reactions (39,40,42). The mean particle diameter was regulated by an extrusion method to 265-305 nm to study the influence of [Hb] in , and to 178, 265, and 452 nm at the same [Hb] in (equal to 35 g/dl) to study the influence of the particle diameter (32,34,43,44) (Table 1). After removing the unencapsulated Hb solution using ultracentrifugation, HbV was resuspended in the same PBS solution (pH 7.4) at [heme] ϭ 300 M. Therefore, the carbonylhemoglobin in HbV is converted to HbO 2 by photodissociation of CO by illuminating visible light under O 2 atmosphere. Briefly, an aliquot of CO-bound HbV was put in a glass flask; this was rotated using a rotary evaporator while the flask was immersed in cold water and illuminated using a halogen lamp (500 watts) with a continuous and gentle O 2 flow inside the flask for several minutes. The complete conversion to HbO 2 was confirmed by absorption spectroscopy in the Q band. The physicochemical characteristics of the obtained HbVs are listed in Table 1. The particle size distribution was measured using a dynamic lightscattering method (Submicron Particle Size Analyzer, model N4 PLUS; Beckman-Coulter, Inc., Fullerton, CA). The P 50 values were obtained from the oxygen equilibrium curve measured with a Hemox-Analyzer (TCS Medical Science, Philadelphia, PA); all samples were ϳ13-16 torrs at 37°C.
Stopped-flow Analyses-The time course of the ligand binding was analyzed at a rapid mixing of a deoxygenated HbV solution and a NO-containing or CO-containing solution using a stopped-flow rapid scan spectrophotometer (model RSP-1000; Unisoku Co. Ltd., Osaka, Japan). Solutions in the two reservoirs (A and B) are mixed rapidly with an applied pressure of 0.3-0.6 megapascals and a dead time for mixing of Ͻ1.5 ms. All measurements were performed at 25°C. A PBS solution (3 ml each) was poured into both reservoirs and sealed using septum rubber seals. The reservoirs were deoxygenated by N 2 bubbling for over 30 min for the complete removal of O 2 . This is important in the case of NO bubbling to prevent the NO loss and metHb formation. The HbV stock solution (ϳ30 l, [heme] ϭ 300 M) was injected into Reservoir A to adjust [heme] finally to 3 M; the N 2 bubbling was changed to flowing to avoid denaturation of the solutes. Complete deoxygenation was confirmed using preliminary stopped-flow measurements (wavelength: 385-593 nm), where the Soret band showed a maximum absorption ( max ) at 430 nm attributable to the presence of deoxyHb. In Reservoir B, NO or CO gas bubbling was started; a gentle N 2 flowing was maintained in Reservoir A. The mixed gases for NO binding (NO, 0.2029%; N 2 , 99.7971%) and for CO binding (CO, 14.14%; N 2 , 85.86%) were purchased from Takachiho Chemical Industrial Co., Ltd. (Tokyo). After about 10 min of bubbling, stopped flow measurement was initiated. The sampling interval and the exposure time were set as 1 ms. The measurement time was 210 ms. All measurements were performed three times, and the change of absorbance at 430 nm was plotted as a function of time. The apparent binding rate constants of NO and CO (kЈ on (NO) , and kЈ on (CO) , respectively) were calculated using Equation 1 under the assumption of homogeneous distribution Physicochemical characterization of a series of HbV prepared for the stopped flow spectrophotometry to observe the NO and CO binding profiles  were used to examine the influence of intracellular Hb concentration (͓Hb͔ in ). Samples 4 -6 were used to study the influence of particle diameter. The P 50 value (oxygen tension at which Hb is half-saturated with oxygen) were regulated in the narrow range of 13-16 torrs to minimize the influence of Hb allostery on the binding rate constants of NO and CO. of Hb, irreversible second order reaction, and pseudo-first-order reaction when gas molecules are abundant, where ⌬A t represents the change of absorbance at 430 nm at time t (equal to A t Ϫ A t ϭ ∞ ), and ⌬A 0 is the absorbance at the initial time (equal to A t ϭ 0 Ϫ A t ϭ ∞ ). C Gas is the initial gas concentration. In the case of the NO binding experiment, NO (1.9 M) is not excessively abundant in comparison with heme concentration (1.5 M); therefore, we calculated the apparent binding rates from the slopes of the initial phase of reactions.
Computer Simulation-We assumed that HbV is spherical and dispersed homogeneously. The gas diffusion constants are much larger than those of Hb molecule (7 nm) and HbV (250 nm) (45). Accordingly, we analyzed only gas diffusion and the formation of ligand-bound Hb in a single HbV particle. We did not consider the extracellular diffusion barrier because of the rapid mixing of small particles, and also we did not consider the gas permeability constant in the lipid bilayer, because the thickness of the lipid bilayer (ϳ5 nm) is thin in comparison with the particle diameter. (Our results show that they would not be important parameters in our system.) To simplify the equation, the distance from the surface to the core of HbV, 125 nm, was divided by 12.5 nm into 10 units. For simulation of a larger particle, such as that with an 8000-nm diameter, 4000 nm was divided by 12.5 nm into 320 units. The first unit is located at the HbV surface and is in the concentration boundary condition. The last unit is located in the core of HbV in the closed condition. From the gas diffusion equation (Equation 2), the onedimensional diffusion from the surface to the core of the particle can be expressed as Equation 3, where C Gas (t i , x j ) represents the gas concentration at time i (t i ) in 1 unit (x j ; distance from the surface of HbV); ⌬C Gas (t i , x j ) is a mass change by diffusion; A j is the interface area of the units j Ϫ 1 and j, and it changes with the distance from the core of HbV; ⌬t is the step time; V j is the volume of the unit j; and ⌬x is the distance between neighboring units. A gas molecule reacts with a heme in Hb. We assumed that the reaction is irreversible. Therefore, the changes of concentrations are expressed as Equations 4 and 5 with a binding rate constant, k on , of an elementary gas binding reaction.
At a step time ⌬t and in a step unit ⌬x, the changes of concen-trations (⌬C heme , ⌬CЈ Gas ) by the gas bindings are expressed as Equations 6 and 7.
At the onset of reaction by mixing two solutions in the stoppedflow apparatus, the gas diffuses into the HbV. Therefore, the initial unbound free gas concentration inside the vesicle is assumed to be zero. The initial unbound free heme concentrations of HbV are 620 -21,700 M ([Hb] in ϭ 1-35 g/dl); they decrease with the reactions of gas molecules. All initial values for calculations are summarized in Table 2. The diffusion constant of the Hb molecule is concentration-dependent and decreases from 77 to 7.4 m 2 s Ϫ1 with increasing [Hb] in from 1 to 35 g/dl (46 -48). The diffusion constants of gases are 2 orders larger than that of Hb. The diffusion constant of O 2 in Hb solutions (D O 2 ) decreases with increasing Hb concentration. The diffusion constants of CO and NO (D NO and D CO , respectively) are calculated from D O 2 using Equation 8 (2), where MW x is the molecular weight of NO or CO. One-dimensional diffusion simulation coupled with gas binding reactions was performed based on the equations given above (Equations 3, 6, and 7) according to the finite differential method using a Visual Basic Language Programming (Excel, Microsoft Corp., Japan, Tokyo) in a personal computer. Both C Gas and C heme at t i were calculated using those at t i Ϫ 1 . Both ⌬C heme and ⌬CЈ Gas were calculated using Equations 6 and 7. Gas molecules diffuse depending on a concentration gradient, and the obtained ⌬C Gas of Equation 3 was combined with ⌬CЈ Gas of Equation 7 for the next step calculation of C Gas . The time interval, ⌬t, was set as 0.01 s, and 10 7 steps were required to calculate the reaction profile for 100 ms in the case of HbV with a 250-nm diameter. The data were output at every 5 ms.
As the reaction proceeds, the concentration of gas in the bulk solution decreases. To reflect this, Equation 9 is used, where the following variables are used. C 0 (Gas) is the initial gas concentration; C 2 (Gas) is at the boundary condition (in the bulk solution); C 1 (GasTotal) is the sum of the bound and unbound gas molecules in HbV; C o (heme) is the total heme concentration in the solution (1.5 M); and C 1 (heme) is the heme concentration in HbV (such as 21,700 M at [Hb] in ϭ 35 g/dl). The level of unbound free heme, R, can be expressed as Equation 10, which is used to calculate the levels of reactions for 100 ms and the apparent rate constants from the initial slopes (5 ms).

NO Binding and CO Binding Profiles of HbV Using
Stoppedflow Spectrophotometry-The complete deoxygenation of HbV was clearly confirmed according to the characteristic wavelength of the maximum absorption ( max ) at 430 nm. Because of the strong light-scattering effect of the HbV suspension in comparison with Hb solution and RBC (49), the absorption peaks in the Q band region were not clear in this measurement. After rapid mixing with NO, the immediate absorbance reduction at 430 nm and the increase at 418 nm that correspond to the formation of nitrosylhemoglobin were confirmed (Fig. 1). In the case of mixing with CO, the immediate absorption increase at 419 nm was confirmed. The change of absorption at 430 nm in both reactions was single exponential and indicative of the formation of nitrosylhemoglobin or carbonylhemoglobin in the vesicles.
Time Courses of NO Binding and CO Binding to HbV with Various [Hb] in -The scans of spectrophotometry in Fig. 1 were performed three times, and the average level of reaction was plotted as a ratio of absorbance at 430 nm (⌬A t ) at time t, to the initial absorbance (⌬A 0 ) at time 0 (Fig. 2). The graph shows that the NO binding is retarded with increasing [Hb] in from 1 to 35 g/dl. However, no such change was observed in the case of CO binding. From the slopes shown in Fig. 2 (50,100,200,250, and 500 nm) were performed, and the obtained kЈ on (NO) and kЈ on (CO) were plotted on Fig. 3. It was clearly recreated that the NO binding is influenced significantly by [Hb] in and the particle size. Although there were deviations from the experimental results, the NO binding was retarded with increasing [Hb] in from 1 to 35 g/dl. On the other hand, no such change existed in the case of CO binding, and the simulations fit well with the experimental results (Fig. 3A). The size dependence of kЈ on (NO) and the independence of kЈ on (CO) were also recreated well as shown in Fig. 3B. The larger particle showed a slower rate of NO binding but not CO binding. It should be noted that this simulation does not consider the extracellular diffusion barrier and lipid membrane permeability.
The one-dimensional concentration changes of free NO molecules and unbound free hemes in each unit in one HbV ([Hb] in ϭ 1 and 35 g/dl) are obtained by simulations, and the results are converted to a two-dimensional scheme, as shown in Fig. 4. In the case of HbV at [Hb] in ϭ 1 g/dl, both dissolved free NO and unbound free hemes are already homogeneously distributed at 5 ms, indicating that NO diffuses rapidly into HbV, and the reaction proceeds quite homogeneously. On the other hand, HbV at [Hb] in ϭ 35 g/dl showed heterogeneous distribution. The concentration gradients of both NO and heme change from the interior surface to the core. Even after 100 ms, the distributions are heterogeneous.
To clarify the influence of D NO that changes with [Hb] in (Table 2), D NO was fixed to the value in the bulk solution (2210 m 2 s Ϫ1 ) to all HbV with different [Hb] in . As shown in Fig. 5, the difference in kЈ on (NO) is minimized considerably in comparison with the condition of variable D NO at each [Hb] in . This indicates that the lowered D NO in the highly concentrated viscous Hb solution contributes considerably to the retardation of NO binding.
Extrapolation to Larger Particles (1000 -8000 nm)-Computer simulations were performed to larger particles (diameter, 1000, 2000, and 8000 nm) in addition to smaller particles (Յ500 nm); their apparent binding rate constants, kЈ on (NO) and kЈ on (CO) , are plotted against the diameter to clarify the influence of diameters of particles encapsulating the 1 and 35 g/dl Hb solutions (Fig. 6). The experimental values of the Hb solution and HbV are also plotted; they show good coincidence. At [Hb] in ϭ 35 g/dl, both NO binding and CO binding are remarkably retarded with larger diameters. Interestingly, there were threshold diameters for retardation of both NO and CO bindings, around 100 nm for kЈ on (NO) and 1000 nm for kЈ on (CO) . Although HbV with smaller diameters shows almost identical kЈ on (CO) , the results of our computer simulation suggest that particles larger than 1000 nm would show retardation of CO binding in much the same manner as that with NO binding. At [Hb] in ϭ 1 g/dl, both NO binding and CO binding showed less change in the binding rate constants that coincide the experimental results; however, the simulation predicts that the retardation becomes obvious with particles larger than ϳ1000 nm for NO binding, and  ϳ2000 nm for CO binding. We can estimate the apparent binding rate constant of a particle encapsulating a 35-g/dl Hb solution with 8000-nm diameter, and kЈ on (NO) and kЈ on (CO) will be reduced to 5.6 ϫ 10 5 and 7.3 ϫ 10 4 M Ϫ1 s Ϫ1 , respectively. Overall, encapsulation of a 35-g/dl Hb solution in an 8000-nm particle would retard the NO binding by 2 orders and the CO binding by 1 order in comparison with the corresponding elementary reactions of the cell-free Hb solution.

DISCUSSION
Our primary finding is that NO binding of Hb is considerably retarded when a concentrated Hb solution is encapsulated in phospholipid vesicles (liposomes). On the other hand, CO binding of Hb shows no such retardation by encapsulation with particle size smaller than 500 nm. The phospholipid bilayer membrane itself has no barrier function to the gas diffusion, because the apparent binding rate constants of both NO and CO at [Hb] in ϭ 1 g/dl and those of an acellular Hb solution were almost identical. In this study, using computer simulations, we propose that the determinant factor of retardation should be the intracellular, not extracellular, gas diffusion barrier in the case of HbV, which was induced by (i) the considerably large binding rate constant of NO to a heme of an Hb molecule, (ii) the numerous hemes as sites of gas entrapment at a high [Hb] in , (iii) the slowed gas diffusion in the intracellular viscous Hb solution, and (iv) the longer diffusion distance in the larger particle diameter of the capsule (Fig. 7).
We reported the retardation of NO binding by Hb encapsulation in 1996 (30), which was earlier than the 1998 report of Liu et al. (6), who first showed that NO binding of Hb is retarded by the RBC cellular membrane. Rudolph et al. (26) attempted stopped-flow spectrophotometry of liposome-encapsulated Hb in 1997, expecting the retardation of the NO reaction by Hb encapsulation, but they identified no effect that was likely to have been attributable to the low [Hb] in (Ͻ14 g/dl) of their liposome-encapsulated Hb. In the present study, we intended more detailed analyses to clarify the mechanism of retardation, because it seems to have remained controversial in the last decade (20). It seems to us that these controversies are attributable to the complex and fragile structure of RBC and chemically unstable NO, which make it difficult to analyze the NO binding of RBC without causing hemolysis (2,50). So-called competition experiments have been conducted between free Hb and RBC at a high hematocrit that would be a physiologically more relevant condition (7,50). However, it remains unclear for us whether the heterogeneous condition of a concentrated RBC suspension in a more static condition would be appropriate for an accurate kinetic measurement. Resealed RBCs were prepared to reduce the submembrane cytoskeletal layer or to reduce [Hb] in (2, 23), but it remains unknown whether hemolysis was suppressed completely after the complicated procedure and whether the electrolyte concentrations were maintained that might influence the Hb allostery and the resulting ligand binding profiles. We surmised that utilization of HbV, an artificially prepared model of RBC, would enable a systematic analysis, because the physicochemical parameters of HbV are adjustable, such as high [Hb] in up to 35 g/dl and particle diameter in a narrow range of P 50 . Moreover, the physical stability of HbV is unexpectedly sufficient for stopped-flow spectropho-tometry. We intentionally selected a low NO concentration (1.9 M) to monitor the whole reaction of NO binding. Precedent reports of stopped-flow spectrophotometry of RBC at a higher NO concentration presented the problem not only of hemolysis but also the rate of NO reaction. It is so fast that a substantial part of the process occurs during the dead time (1-2 ms). On the other hand, in our study, a pseudo-first-order reaction is not appropriate for NO binding, and we calculated kЈ on (NO) from the initial phase of the reaction because of a low NO concentration compared with the heme concentration. In such a condition, some redox charge transfer reaction would occur between heme and NO at a lower NO concentration (51). Another limitation of our simulation is the wide size distribution of HbV prepared using the extrusion method.
[Hb] in was the concentration of the fed Hb solution for encapsulation, and we did not directly measure [Hb] in after encapsulation. These would be reasons for the deviation of the experimental results and the simplified computer simulation. However, it should be noted that our computer simulations recreated the tendencies of the experimental results of the ligand binding profiles of HbV.
In the computer simulation, we did not include the extracellular diffusion barrier, because HbV (250 nm) is much smaller than RBC (8 m), and the diffusion of HbV as a particle should be much faster than that of RBC according to the Stokes-Einstein equation. The extracellular fluid near the surface should be stirred by the rapid movement of HbV. It is expected that the Diameter (nm) . Computer simulations of NO binding and CO binding by particles with different particle diameter. At [Hb] in ϭ 35 g/dl, the apparent CO binding rate constant, kЈ on (CO) , is almost identical up to 1000 nm in diameter; then it is reduced considerably, concomitant with increasing the diameter (blue squares in the bottom). On the other hand, kЈ on (NO) decreases slightly up to 100 nm diameter; it then decreases steeply with enlarging particle diameter (blue circles in the top). In the case of [Hb] in ϭ 1 g/dl, both NO binding (light blue circles) and CO binding (light blue squares) showed less change in the binding rate constants. However, the retardation becomes obvious when the particle diameter is larger than ϳ1000 nm for NO binding and even for CO binding when the diameter is larger than ϳ2000 nm. Experimental values for the Hb solution (white circle and square) and HbV (pink or red squares and circles) are close to the simulated values. The apparent binding rate constants, kЈ on (NO) and kЈ on (CO) , of a spherical particle with diameter of 8000 nm and [Hb] in ϭ 35 g/dl are estimated to be reduced to 5.6 ϫ 10 5 and 7.3 ϫ 10 4 M Ϫ1 s Ϫ1 , respectively. The reported kЈ on (NO) values of a series of chemically modified HBOCs (diameter, 6 -28 nm), about 3.0 ϫ 10 7 M Ϫ1 s Ϫ1 , were identical to that of an unmodified Hb solution (38), which coincided well with our simulation.  FIGURE 7. Proposed mechanisms of retardation of gas binding by encapsulated Hbs. A, it has been suggested that an unstirred layer near the outer surface of a cell would become an extracellular diffusion barrier to retard ligand bindings. However, our experimental results and computer simulations suggest that this is not a major process for retardation of ligand bindings in the case of HbV. B, the phospholipid bilayer membrane cannot have any barrier function to gas diffusion, because the apparent binding rate constants of both NO and CO at [Hb] in ϭ 1 g/dl were close to those of an acellular Hb solution, as shown in Fig. 3. We propose that the determinant factor of retardation should be the intracellular diffusion barrier in the case of HbV, which is induced by (i) an intrinsically larger binding rate constant of NO to a heme in an Hb molecule, (ii) numerous hemes as sites of gas entrapment at a higher [Hb] in , (iii) a slowed gas diffusion in the intracellular viscous Hb solution, and (iv) a longer gas diffusion distance in a larger capsule.
thickness of the unstirred layer as an extracellular diffusion barrier would be much less for small HbV than that for RBC (1-3 m) (2). Actually, results of the present computer simulations of HbV without consideration of the extracellular diffusion barrier clarified that the intracellular diffusion resistance is sufficient to explain the retardation of NO binding in the results of stopped-flow spectrophotometry, and possibly, our findings might suggest that the extracellular diffusion barrier is negligible even for RBC. This supports the results of Vaughn et al. (7) that the extracellular diffusion resistance is negligible. However, our data do not directly support the presence of transmembrane diffusion limitation, because the HbV at [Hb] in ϭ 1 g/dl and the cell-free Hb solution showed nearly identical kЈ on (NO) ; actually, the computer simulation did not require the consideration of the membrane barrier. Han et al. (23) proposed that a submembrane cytoskeletal barrier would induce the resistance to the NO binding to bovine RBC using the RBC ghost. This might be possible to some extent if the submembrane cytoskeleton were to contain densely layered heme proteins such as adsorbed Hbs that could be the sites of rapidly binding NO. However, we believe that the intracellular concentrated Hb solution (about 35 g/dl) near the cytoskeleton of RBC can be the predominant barrier to further NO diffusion into RBC. Liu et al. (19) described that "NO that enters into RBC is immediately scavenged by the concentrated intracellular Hb so that NO concentration inside the RBC is maintained very close to zero," although they did not pay attention to it as the intracellular diffusion barrier.
The binding rate constant of CO of cell-free Hb molecule (k on (CO) ) is well known to be much smaller than those of NO and O 2 (52). The rate-limiting step for CO binding is the internal bond formation with the heme iron. In fact, based on the electron theory, CO enters the globin hundreds of times before it finally forms a bond with the iron atom. Consequently, the overall bimolecular rate constant is normally small (53). The experimental finding that CO binding shows negligible retardation, even after encapsulation in HbV, also supports our proposal that rapid NO binding causes the sink of NO at the interior surface region of HbV and retards further NO diffusion into the core of HbV in combination of the lowered D NO in the highly concentrated viscous Hb solution (45)(46)(47)(48). However, it is expected that HbV with a much larger diameter can contribute to retardation, even for CO binding, as clarified by our computer simulation. Coin and Olson (2) compared the bindings of O 2 , CO, and ethyl isocyanate to Hb with their elementary reaction constants, k on , of 3 ϫ 10 6 , 2.0 ϫ 10 5 , and 2.1 ϫ 10 4 M Ϫ1 s Ϫ1 , respectively (1:10 and 1:100 differences). Results of that study showed that the difference between k on of Hb and kЈ on of RBC decreases for a slower reaction. The difference becomes very small for the binding of ethyl isocyanate, which clearly supports our data; a faster reaction tends to induce a stronger intracellular diffusion barrier and retards the reaction in comparison with the cell-free Hb solution.
In blood circulation in the presence of O 2 , NO is inactivated mainly by NO dioxygenation by O 2 -bound HBOCs and RBC. According to Herold et al. (54), the rate constant of the elementary reaction, HbO 2 and NO, is 8.9 ϫ 10 7 M Ϫ1 s Ϫ1 , which is faster than that of deoxyHb (2.6 ϫ 10 7 M Ϫ1 s Ϫ1 ). We predict that the reaction with HbO 2 should be much faster to form an intracellular diffusion barrier than that with deoxyHb. Consequently, the contribution of Hb encapsulation to the retardation should be pronounced. This can support the results of Azarov et al. (50) and Huang et al. (21), which showed that "the membrane barrier function" becomes more effective in limiting NO uptake for oxygenated RBC than the deoxygenated RBC, although their proposing mechanism is different from ours. Our computer simulation system would be an effective tool to predict the ligand binding profiles of HbV with different Hb concentration and different particle size and other imaginary parameters. This can roughly simulate the NO binding and CO binding profiles of a spherical particle with a diameter identical to that of the major axis of RBC. The values of kЈ on (NO) and kЈ on (CO) of a spherical particle encapsulating 35-g/dl Hb with a diameter of about 8 m are estimated, respectively, as 5.  (50), which are contradictorily much smaller than the CO binding rate constants of the above, which might suggest the presence of other mechanisms, such as the unstirred layer as the extracellular diffusion barrier in the case of large RBCs that diffuse slowly at a high Hct in their experiments. Even so, the retardation seems to be mainly induced by the intracellular diffusion barrier, because kЈ on (NO) is reduced by 2 orders of magnitude in comparison with a cell-free Hb. Alternatively, we might consider the biconcave disk structure of RBC. Different P 50 values of HbV (13-16 torrs) in comparison with that of human RBC (28 torrs) might also influence the binding rates.
Interestingly, the presence of the threshold diameters for retardation of ligand bindings is apparent, as shown in Fig. 6. The threshold diameter for CO is larger than that for NO, indicating that the slower reaction of CO binding allows a longer distance of gas diffusion before induction of an intracellular diffusion barrier than it allows with the more rapid NO binding. The rate-determining steps are the elementary gas-binding reaction for particles smaller than the threshold diameter and the gas diffusion for larger particles. It should be noted that the retardation is predicted for the larger particles at [Hb] in ϭ 1 g/dl, although the threshold diameter is increased to 1000 nm for NO binding and 2000 nm for CO binding.
The retardation of NO binding by Hb encapsulation cannot fully explain the phenomenon that HbV with a diameter of ϳ250 nm does not induce vasoconstriction after intravenous injection (13), because kЈ on (NO) of HbV is much larger than that of RBC (10 4 to 10 5 M Ϫ1 s Ϫ1 ). Any HBOC is much smaller in size than RBC and is distributed homogeneously in the plasma layer (5). Therefore, an RBC-free zone at the blood/endothelium interface becomes an HBOC-dissolved zone and might be a sink of NO (56,57). Rohlfs et al. (38) reported that the NO binding rate constants of a series of chemically modified HBOCs (diameter, 6 -28 nm) (58), measured using the laser flash photolysis, were identical to that of an unmodified Hb solution, about 3.0 ϫ 10 7 M Ϫ1 s Ϫ1 , which coincided well with our simulation in Fig. 6; particles with a diameter of less than 50 nm are almost identical. They concluded straightforwardly that NO uptake was not related to vasoconstriction, because polyethylene glycol-modified Hb did not exceptionally induce vasoconstriction, and other mechanisms are actually suggested in relation to molecular recognition and oxygen affinity (11,59). We speculate the presence of another threshold particle diameter to penetrate across the perforated endothelial cell layer to approach a space (such as the space of Disse near the sinusoidal endothelial layer in a hepatic microcirculation or the space between the endothelium and the smooth muscle) where CO or NO is produced as a vasorelaxation factor to bind to soluble guanylate cyclase, which catalyzes the conversion of guanosine triphosphate to cyclic guanosine monophosphate (13,18,60,61). As summarized by Olson et al. (16), both the retardation of the NO reaction (reduced NO affinity) (62) and the larger particle diameter are inferred to be keys to suppress vasoconstriction and hypertension induced by HBOCs.
In summary, we suggest the significant contribution of the intracellular diffusion barrier and the absence of lipid membrane barrier for NO uptake in the case of HbV. We speculate that the same findings might apply to RBCs. Although some discrepancies exist between the experimental results and computer simulations, we are surprised that such a simple simulation system can be an effective tool to predict the ligand binding reaction of HbV and larger particles, although the system is based merely on physicochemical parameters: the gas diffusion constant and elementary reaction rate constants. Our data provide a new insight into the cellular structures of RBC and HbV as an artificial oxygen carrier. Our next step will be to apply this system to recreate the ligand binding profiles of a biconcave disk shaped or parachute-like RBC and HbV suspension flowing heterogeneously in microvessels and in an artificial gaspermeable narrow tube (5) to identify additional mechanisms of the absence of vasoconstriction.