Physical and Mechanobiological Basis of Biological Functions of Platelets

Abstract

Platelets play a unique role in thrombosis and hemostasis. Historical research has revealed biological mechanisms underlying various platelet functions. However, unraveling the complex mechanisms underlying various platelet functions is challenging. Recent progress in high-performance computer has enabled an understanding of the complex biological functions of platelets through combinations of basic principles of physics, such as Newton's laws of motion, fluid mechanics, and mechanobiology. Platelets are blood cells with diameters of 2 to 5 µm. They lack nuclei but contain organelles such as mitochondria. Platelets promptly adhere to the sites of endothelial damage for hemostasis. Adherent platelets are activated to allow plasma ligands of fibrinogen and von Willebrand factor (VWF) to bind stably to them. They also enhance local coagulant activity through their procoagulant activity. The specific biological functions of platelets are mediated by dynamic structural changes in their membrane proteins. Even lipids and proteins that mediate the specific functions of platelets are constructed from atoms following basic physical rules, such as Newton's laws of motion. Thus, the various biological functions of platelets can be constructed from physical principles, starting with the movement of atoms. Here, various complex biological functions of platelets were constructed using mathematical models and simple physical principles. This framework may help explain the complex pathophysiological mechanisms underlying the VWF–platelet interaction in both healthy and diseased conditions. Detailed quantitative biological experiments confirmed the validity of these mathematical models. The future direction of constructive “theoretical medicine and biology,” starting from atomic movements, is expected to follow.

 

MissingLinkText

Keywords

platelets - adhesion - von Willebrand factor - GPIbα - GPIIb/IIIa - molecular dynamic simulation - high-performance computer

Biological Role of Platelets

Platelets are small cells without nuclei and do not have the potential to differentiate or divide; however, they contain other subcellular organs, including the mitochondria and Golgi apparatus.[1] The shape of non-activated platelets is discoid with a diameter of 2 to 5 µm.[2] However, it changes substantially after activation.[3] The concentration of platelets in humans is approximately 200 × 10³/µL, and the total volume of platelets in circulating blood is small compared to the other blood cell types, including erythrocytes. Platelets play crucial roles in hemostasis and thrombus formation.[4] [5] [6]

Recent progress in biological research has revealed that the biological functions of platelets extend beyond hemostasis or thrombus formation,[7] [8] [9] including regulating inflammation,[10] [11] [12] various immunological functions,[13] [14] [15] [16] [17] [18] and maintaining microcirculations.[19] [20] Recent progress in single-molecule biophysics has further revealed the biomechanical behavior of platelets.[8] [9] The physical basis of the biological functions of platelets will be discussed in this review.

 

MissingLinkText

Physical Basis of Platelet Adhesion

Biological reactions, including platelet activation, require more time than simple physical phenomena. Hemostatic reactions begin immediately to avoid the loss of blood components when blood vessels are injured. Accordingly, simple physical reactions are more suitable than complicated biological mechanisms for rapid hemostasis. Indeed, biological experiments have revealed that platelet adhesion occurs at sites of endothelial damage with almost no delay.[21] [22] The prompt platelet adhesion is most likely mediated by simple physical reactions rather than biological mechanisms. Supporting this idea, experiments have shown that platelets tend to flow adjacent to the vessel wall owing to the axial accumulation of erythrocytes ([Fig. 1A]). The large and heavy erythrocytes accumulate at the center of blood flow by Fåhræus's effect in microcirculation.[23] [24] This axis concentration of erythrocytes has been known since the 18th century.[25] Platelets are smaller and lighter than erythrocytes. They are pushed toward the vessel wall by the fluctuating movement of erythrocytes. These biological findings were supported theoretically by computer simulation calculations based on fluid mechanics.[26] [27] The validity of the calculation results of hematocrit-dependent increase in the rate of platelet adhesion was confirmed by quantitative biological experiments using human blood and a rectangular flow chamber with statistical correlation analysis.[27]

Fig. 1 Platelet Adhesion at Sites of Endothelial Damage Under Blood Flow Conditions. (A) Heterogenous distributions of blood cells in flowing blood. Owing to the effects of blood flow, the distribution of circulating blood cells is inhomogeneous. Red cells tend to stay in the center of blood flow due to Fåhræu effects.[23] Then platelets are pushed in the direction of the vessel wall by erythrocytes, as shown by the purple arrows. (B) Mechanism of platelet adhesion to the sites with endothelial injury. The vessel wall is covered by endothelial cells that prevent platelet interaction with the subendothelial matrix. (1) Of the subendothelial matrix, the von Willebrand factor (VWF) plays a crucial role in capturing platelets flowing to the vessel wall. Platelets express the VWF receptor glycoprotein (GP) Ibα in a constitutively active conformation. Once endothelial cells are disrupted by physical (2) or biochemical stimulation (3), platelet adhesion begins promptly upon exposure of VWF to the bloodstream. Flowing platelets possessing flow vectors toward the vessel wall, as shown by the purple arrows, enable platelets to adhere to the site of endothelial injury through simple physical phenomena. (C) Mechanism of single platelet adhesion on VWF exposed at the sites of endothelial injuries. VWF molecules have multimeric structures. Platelet GPIbα molecules are heterogeneously expressed. Most likely, the GPIbα molecules that are densely expressed on flowing platelets transiently bind to a single subunit of VWF expressed on the vessel wall. When the number of bonds formed between VWF and GPIbα becomes sufficiently large to produce a binding force strong enough to resist the fluid dynamic detaching force, the platelets apparently adhere to the site of the injured vessel wall. The fluid dynamic forces applied to the platelets and heterogeneous cytoskeletal tension result in the elongation of the platelets, forming pseudopods (shown as blue rectangles) to support their binding to the vessel wall. Notably, the GPIbα–VWF bond was always transient, with a high off-rate.

Owing to the effects of the axis concentration of erythrocytes, platelets are pushed toward the blood vessel wall and collide regularly with it. However, platelets do not adhere to vessel walls in the presence of healthy functioning endothelial cells. In other words, endothelial cells protect vessel walls from platelet adhesion.[28] Once endothelial cell function is impaired, platelet adhesion begins.[21] [22] These phenomena support the mechanism of platelet adhesion as summarized in [Fig. 1B]. Flowing platelets have a velocity vector toward the vessel wall generated by positional fluctuations of heavy erythrocytes flowing in the center of the blood flow.[26] [27] Platelets express receptors for von Willebrand factor (VWF), namely, glycoprotein (GP) Ibα, in a conformation ready to bind with VWF.[29] The healthy endothelial cells cover VWF to prevent platelet adhesion to the vessel wall.[21] [30] All these important premises for the mechanism summarized in [Fig. 1B] have been proven biologically.

VWF is an important ligand for platelet adhesion and cohesion under blood flow.[31] It is produced constitutively from endothelial cells[32] or stored in either Weibel-Palade bodies in endothelial cells or α-granules in platelets or megakaryocytes.[33] [34] These stored VWFs are released upon stimulation. In endothelial cells, the prompt extracellular translocation of VWF occurs after stimulation.[22] [35] [36] Platelet adhesion to stimulated endothelial cells follows simultaneously.[21] [22] When endothelial cell disruption occurs, VWF accumulated in the subendothelial matrix is exposed to the bloodstream with other thrombogenic substances such as collagen.[30] [32] [37] [38] [39] [40] Once VWF is expressed at the vessel wall, platelet adhesion occurs promptly mediated by VWF binding with GPIbα.[1] A previous study suggested that platelet adhesion to the vessel wall can be simulated quantitatively using a kinetic Monte Carlo lattice model. Three types of events, including GPIbα diffusion, GPIbα–VWF bond formation, and their breakage, were included in their model. Simulation calculations suggested the importance of GPIbα localization compared to the probability of GPIbα–VWF bond formation in the adhesion force generated between the platelet and the vessel wall.[41]

Single platelet cells express approximately 15,000 molecules of GPIbα.[29] It is important to note that the distribution of GPIbα expression on single platelets is heterogeneous, meaning that the GPIbα expression is concentrated in some regions of the platelet membrane.[1] Molecular dynamic simulation calculations and biological validation experiments revealed that a single bond of GPIbα–VWF generates binding forces of 50 to 100 pN.[42] [43] [44] Because platelets adhered on VWF at a wall shear rate of 1,500 s⁻¹ are exposed to a detaching force close to a few hundred pN,[45] only a few molecules out of the 15,000 GPIbα bound with VWF are necessary and sufficient for platelet adhesion to the vessel wall resistant to the detaching force generated by blood flow. The physical mechanism of single platelet binding to the vessel wall is summarized in [Fig. 1C]. In summary, the membrane expression of GPIbα is heterogeneous, and only a few GPIbα molecules bind to VWF at the nanometer scale, supporting single-micrometer-scale platelet adhesion at sites of the injured vessel wall. Because platelets start to adhere to the vessel wall in the region where GPIbα molecules are densely expressed, platelet adhesion is often supported by pseudopods formed by the elongation of the platelet membrane due to the effects of fluid dynamic force and the heterogeneity of cytoskeletal tensions as mechanobiological responses[46] ([Fig. 1C]).

 

MissingLinkText

Physical Basis of Platelet Adhesive Protein Functions

The biological functions of various macromolecules, such as platelet GPIbα, are complex. Indeed, GPIbα is the main player in platelet adhesion at sites of endothelial damage under blood flow conditions.[31] [47] Even though apparently complicated, the biological functions of various macromolecules should depend on the simple physical characteristics of the atoms constructing them. In simplified physics, atomic characteristics can be described by three parameters: (1) mass, (2) position coordinates, and (3) velocity. Accordingly, the physical characteristics of molecules can be described by integrating the positional coordinates and velocity vectors of atoms of various masses. Recent progress in high-performance computers has enabled the calculation of such parameters for all atoms constituting macromolecules with specific biological functions using a simple physical law, Newton's Second Law of F (force) = M (mass) × A (acceleration). Each atom in a molecule has its own initial position coordinate. Owing to heat and interactions with other atoms, each atom faces various forces, including the van der Waals force, Coulomb force, and universal gravitation. Around the target molecule, the force fields in which the forces act on the target atoms are uniquely determined by their relative positions. Among the various force fields, the CHARMM (Chemistry at HARvard Macromolecular Mechanic) force field, where quantum mechanics is incorporated into the Newtonian force field as a rotating and progressing spring, is popularly used.[48] [49] [50] [51] [52] The forces on all the atoms constructing the molecules are determined by the CHARMM force field. Then the position coordinates and velocity vectors of all the atoms constructing the molecule were updated in a stepwise manner following the equation F (force) = M (mass) × A (acceleration). Typically, small changes in the position coordinate and velocity vectors of each atom are calculated every 2 × 10⁻¹⁵ sec. Through integrated calculations, the physical parameters of platelet GPIbα binding with VWF, including binding structures, energies, and forces, can be calculated.[42] [53]

The calculation of the force generated between GPIbα and VWF should be conducted under the strict conditions shown in [Fig. 2]. [Fig. 2A] shows the positions of GPIbα and VWF with a mass distance of d. The potential of mean force (PMF) between GPIbα binding and VWF (which can then be used to calculate the binding energy) becomes lowest at a mass distance of d. Then the PMF was calculated when the mass centers of GPIbα and VWF were gradually separated in each by 0.5Å. Finally, the distance between the two molecules becomes sufficiently large such that physical interactions are no longer present ([Fig. 2C]). Based on the calculated relationship between the mass center distance between GPIbα and VWF and the corresponding PMF, the binding force between GPIbα and VWF was 63.4 pN.[42] This value may not be the same as the binding force generated between GPIbα and VWF when platelet adhesion to VWF occurs under blood flow conditions. However, this value is still meaningful because it reflects the potential binding energy between the GPIbα and VWF bonds, and the values can be validated biochemically using other experimental methods. The predicted binding force (63.4 pN) is within the order of magnitude of the values experimentally measured with an optical tweeter and an atomic force microscope.[43] [44]

Fig. 2 Physical Characteristics of GPIbα–Von Willebrand Factor (VWF) Bond. The structural energy expressed as the potential of mean force (PMF) in the GPIbα–VWF bond becomes the lowest in the absence of an external force when the distance of the mass of each molecule is d. (A) When the detaching force is applied to the mass centers of GPIbα and VWF in the direction of the orange dotted lines, the shapes of GPIbα and VWF are influenced by the effects of these external forces. The PMF of the GPIbα–VWF bonds increased with increasing distance between the mass centers of GPIbα and VWF, relative to d' (B). When the distances between the molecules reach the threshold (d''), they no longer interact with each other and detach (C). (D–F) The relationship between the PFM of the GPIbα–VWF bonds and the mass distances between GPIbα and VWF.

Because platelets adhered to the site of endothelial injury face a fluid dynamic force of approximately 100 pN at a wall shear rate of 1,500 s⁻¹, several pairs of GPIbα–VWF bonds should produce a sufficient binding force to resist detachment from the vessel wall due to the detaching force generated by blood flow ([Fig. 1C]).[27] It is important to note that the GPIbα–VWF bond is not stable but only transient.[47] Accordingly, the number of GPIbα–VWF bonds formed at any given moment is probability-dependent. The actual behavior of platelets binding to VWF under flow conditions could be predicted using a multiscale model for shear-mediated platelet adhesion dynamics, which integrated dissipative particle dynamics (DPD) and coarse-grained molecular dynamics (CGMD) to describe molecular-scale intraplatelet constituents and their interactions with the surrounding flow using lattice kinetic Monte Carlo methods.[54]

 

MissingLinkText

Physical Basis of the Effects of Blood Flow on Platelet Adhesion

Coronary stent implantation is commonly performed to treat acute myocardial infarction and unstable angina.[30] [55] [56] [57] [58] These stent implantations often result in blood flow disturbance ([Fig. 3]). The stent struts located at the vessel wall disturb blood flow locally. Platelets flowing to the center of the blood flow, owing to the presence of stent struts, are pushed back by the effects of centrally flowing heavy erythrocytes. This results in greater platelet accumulation distal to the stent strut.[4] [59] The shape of the stent strut largely influenced the amount of platelet accumulation downstream of the stent strut.[60] Computer simulations of platelets confirmed the physical basis of stent-induced platelet accumulation.[61]

Fig. 3 Platelet Accumulation Around Stent Struts. Stent struts were implanted into the vessel walls. Parts of the struts appear in the flow routes and disturb the local blood flow. Owing to the axial accumulation, erythrocytes flow at the center of the blood flow. Platelet flow adjacent to the vessel wall owing to the effects of the stent struts; platelets flowing adjacent to the vessel wall were pushed toward the center of the blood flow around the stent struts. Subsequently, the platelets moving toward the center of the blood flow are pushed back in the direction of the vessel wall by the effects of heavy erythrocytes in the center. As a result, increased platelet accumulation occurred downstream of the stent struts.

The role of blood flow in platelet adhesion differed substantially before and after platelet adhesion. Before platelet adhesion is completed, the major role of blood flow is to transport circulating platelets to the site of endothelial damage,[62] thus contributing to thrombus formation and growth. The direction of blood flow components toward the vessel wall is helpful for platelet adhesion. After platelet adhesion is complete, the major role of blood flow changes from enhancing platelet thrombus growth to detaching the platelets that have already adhered to the vessel wall.[63] [64] Thus, the fluid dynamic force rather contributes to thrombus dissociation.[4] The integrated strength of the fluid dynamic force applied to the platelets should be equivalent to (or less than) the integrated strength of the binding force generated by the interaction of the adhesive protein with ligands. [Fig. 4] is a simple model that supports platelets with two GPIbα molecules bound to VWF located at the vessel wall. Most likely, the fluid dynamic force applied to platelets changes over time because of the pulsatile nature of blood flow. However, the total force applied to the platelets (fluid dynamic force A) should be less than the adhesion force B plus C to keep the platelets bound to the vessel wall. The easiest way to increase the binding force at B and C after a sudden increase in force A by pulsatile flow is to increase the length of pseudopods B or C to increase the spring force. Biological experiments have revealed the presence of pseudopods that support platelet adhesion.[46] Moreover, both the number and length of pseudopods increased when the probability of GPIbα binding to VWF was blocked by an antibody against VWF.[46] The inhomogeneous distribution of GPIbα on platelets aids in pseudopod length-mediated force adjustment mechanisms.[1]

Fig. 4 Balance of Forces Supporting Platelet Adhesion Mediated by GPIbα–Von Willebrand Factor (VWF) and the Hydrodynamic Detaching Force Generated by Blood Flow. Platelets adhering to the site of endothelial damage experience a fluid dynamic force that detaches them from the vessel wall. (Force A) Platelet adhesion is supported by the force generated by GPIbα binding to VWF. (Force B and Force C) Platelet adhesion persists as long as the integrated force of GPIbα–VWF is greater than that of the detaching force.

The blood flow-dependent movements of the platelets were mathematically modeled as previously described.[61] [65] The initial model treated platelets as particles that adhere to the site of vessel injury. The binding characteristics of the particles after initial adhesion were modeled to represent the results of the biological experiments. These simple platelet models reproduced the markedly greater platelet accumulation downstream of the stent struts[61] and the antiplatelet effects of GPIIb/IIIa and P2Y₁₂ ADP receptor blockers ([Supplementary Fig. S1], available in the online version).[66] Then the particle model of platelets was extended to a voxel simulator.[1] The expansion from a simple particle model to a voxel simulator enabled the representation of heterogeneous distributions of various platelet functional proteins, such as GPIbα. GPIbα was represented by a small number of particles located in the cell membrane. Once the particle was bound to the injured vessel wall, a pseudopod with spring elongation was formed to support platelet adhesion, as shown in [Supplementary Fig. S2] (available in the online version). The developed voxel model divided single platelets into 20 × 20 × 40 voxels. This only represents a rough picture of platelet function constructed from regions with heterogeneous biological characteristics. Further development of a detailed model that separates the platelets into distinct regions representing the functions of various molecules is required.

 

MissingLinkText

Physical Basis of Platelet Activation

Upon activation, platelets undergo substantial changes in their shape and biological functions.[67] [68] [69] [70] [71] Numerous biological events occur in the platelets upon activation. Of these, an increase in the intracellular calcium ion concentration ([Ca²⁺] _i ) is noteworthy.[72] [73] [74] Intracellular calcium-dependent protein kinase mediates the phosphorylation of various intracellular proteins.[75] [76] Platelet adhesion mediated by GPIbα binding with VWF exposed at the site of endothelial injury could also be expressed in a voxel simulator.[1] In this model, activation signals are generated locally around GPIbα molecules interacting with VWF. The spread velocities of the activation signals were determined based on the velocity of the intracellular spread of the increased [Ca²⁺] _i .[72] Once the activation signal(s) reached the region of the platelet membrane, GPIIb/IIIa was activated. All platelets were activated when activation signals are spread throughout the platelet. Subsequently, other flowing platelets began interacting with the platelets that are stably bound at the site of endothelial damage. This simple particle simulator can be expanded to a cell scale using a voxel model.[1] These small changes in the intracellular proteins can provide a driving force for large structural and functional changes in the extracellular domains of membrane proteins.[77]

The affinity of plasma ligand proteins to platelets (such as fibrinogen or VWF) increases substantially when platelets are activated.[78] [79] [80] These ligand proteins bind with platelet GPIIb/IIIa (integrin α_IIbβ₃) only when platelets are activated. These activation-dependent changes in the affinity of integrin α_IIbβ₃ is driven by the structural changes in their extracellular domain.[72] [78] [81] [82] However, the physical basis of the activation-dependent structural changes in the extracellular domain of GPIIb/IIIa is still to be elucidated.

Biological experiments revealed that the intracellular environment of platelets changes substantially upon activation.[72] [83] [84] The “molecular leverage” hypothesis was proposed for linking physical events occurring inside to the outside of platelet cells. Based on this hypothesis, the mechanism of large structural changes in the extracellular domain of GP IIb/IIIa in response to small structural changes in their intracellular domains could potentially be explained[77] ([Fig. 5]). The leverage is composed of the cellular membrane as the fulcrum of the lever. Small structural changes in the intracellular force point representing the intracellular domain of GP IIb/IIIa resulted in substantial structural changes in the extracellular force point representing the extracellular domain ([Fig. 5]). The similar “molecular leverage” mechanism may mediate various functional changes in various cells not limited to platelets. The biological events that occur inside and outside platelets upon activation have been elucidated through various biological experiments. However, it should be noted that “molecular leverage” remains a hypothesis, and further quantitative modeling and validation experiments are required to validate this hypothesis as a true mechanism of platelet activation.

Fig. 5 Molecular Leverage Mechanism Linking the Small Intracellular Structural Changes with Substantial Changes in the Extracellular Domain of GPIIb/IIIa. According to the molecular leverage hypothesis, the intracellular domain of GPIIb/IIIa is structurally flexible in non-activated platelets. (A) The rapid increase in intracellular calcium ion concentrations caused small structural changes in signaling proteins that could bind to the intracellular domain of GPIIb/IIIa. The structural flexibility of the intracellular domain of GP IIb/IIIa is reduced by binding to activated signal proteins. (B) Then the small structural changes in the intracellular domains of GPIIb/IIIa result in substantial structural changes in the extracellular domains of GPIIb/IIIa as a result of molecular leverage.

Another important functional change in platelets upon activation is an increase in their procoagulant activity.[85] [86] [87] [88] In addition to microparticle release, the extracellular expression of negatively charged phospholipids such as phosphatidylserine (POPS) increases substantially with platelet activation.[89] [90] [91] [92] Biological experiments revealed the increased POPS expression on activated platelets.[66] [93] Yet, the mechanism is still to be elucidated. POPS expression is likely associated with an increase in intracellular calcium ion concentration. However, the link between increased [Ca²⁺] _i and the extracellular expression of POPS is unknown. Biochemical experiments revealed the important role of transmembrane protein 16F (TMEM16F) as a phospholipid scramblase.[92] [94]

Activated platelet-derived procoagulant activity was modeled as shown in [Fig. 6]. The initial event is always endothelial disruption. Subsequently, non-activated platelets promptly adhered to the site of endothelial damage. They are activated by interactions between collagen and VWF. Negatively charged POPS phospholipids are expressed externally in the lipid bilayers of activated platelets. Subsequently, various coagulation factors, including those with Gla domains, such as activated factor X (FXa),[95] [96] [97] [98] and those without Gla domains, such as coagulation factor V (FV), accumulate to form the prothrombinase (PT) complex.[90] [99] [100] [101] Prothrombin can be converted efficiently to thrombin by the effects of PT complex. Thrombi then became larger by interacting with platelets and fibrin. This thrombus formation process can be mathematically simulated using a computer simulator.[102]

Fig. 6 The Model Interplay Between Platelets and Coagulation System. Once non-activated platelets adhere to the von Willebrand factor (VWF) exposed at the site of endothelial damage, they are activated by interactions with VWF, collagen, and other soluble factors, such as ADP. Negatively charged phospholipids such as phosphatidylserine (POPS) are expressed on the outside of the activated platelet membranes, as shown in the magnified image in the blue circle. Various coagulation factors, such as activated factor X (FXa) and FVa, accumulate around the POPS to form the prothrombinase (PT) complex. Conversion from prothrombin to thrombin occurs efficiently in the PC complex to form fibrin around activated platelets. POPC, phosphatidylcholine; PT, prothrombinase; TAT, Thrombin antithrombin III complex.

The mechanism of pathological thrombus formation resulting in atherothrombotic events, such as myocardial infarction, can be understood qualitatively, starting from the functions of various proteins and cells.[30] However, there are substantial heterogeneities in the positions and functions of various proteins and cells that make it difficult to establish a simple “theory” for understanding the pathophysiology of various diseases from molecules or cells. Our aim for the next step is to construct pathophysiological events such as myocardial infarction by integrating simple physical equations to develop “theoretical medicine.” Biological cells and molecules are constructed from these atoms. The behavior of atoms depends on simple physical equations, such as Newton's laws of motion. Then the future directions of “theoretical medicine” may depend upon the directional changes from molecular biology to the new era of “atomic biology.” The progression of high-performance computers and information technology may help develop the basis of “atomic biology.” The concept is still highly speculative, and it remains uncertain how precisely we will be able to elucidate the pathophysiology of various diseases in the era of “atomic biology.” Moreover, it remains difficult to foresee how precisely we can predict the future onset of various diseases and the extent to which we can aid in their prevention.

 

MissingLinkText

Physical Basis of Platelet Aggregation

The platelet function was assessed using various biological assays. Platelet aggregation is the most common target in clinical practice.[31] [103] [104] [105] [106] [107] Typically, cloudy platelet-rich plasma (PRP) excluding erythrocytes is prepared. The addition of platelet-activating agents such as ADP, thrombin, or collagen activates platelets in PRP. Once platelets are activated, soluble fibrinogen binds to the activated platelets through their activated GPIIb/IIIa.[78] [79] All soluble factors, including ADP, could reach the platelets by physical diffusion phenomena ([Fig. 7A]). Then external forces such as stirring cause fluid dynamic forces to move activated platelets to collide with each other to form aggregates ([Fig. 7C]). Sizes of platelets with a diameter of 2 to 5 µm are small but not small enough for physical diffusion in the PRP. The extent of platelet aggregation was measured as the light transmittance of the PRP. Light transmittance was low in the cloudy PRP. It increased when the number of particles in the PRP (platelets or platelet aggregates) decreased in the presence of platelet aggregates. The extent of platelet aggregation was calculated by measuring the transmitted light intensity using the Beer–Lambert equation.[107] In this equation, the log (L_t/L_i) = −k × l × c where Lt is the transmitted (L_t) and incident light intensity (L_i), k is the absorption coefficient, l is the effective light pass, and c is the single platelet count. Using constant incident light, the extent of platelet aggregation was calculated.[107] [108]

Fig. 7 Platelet Aggregation. Platelets in platelet-rich plasma (PRP) are activated by the addition of soluble activating agents such as ADP. (A) Soluble fibrinogen (red arrow) binds to activated platelets, as shown in blue (B). Activated platelets form aggregates mediated by fibrinogen (C). The extent of platelet aggregation was calculated from the light transmittance of PRP (D).

Traditional agonist-induced platelet aggregation reflects the physical principles of diffusion of soluble substances and platelet movement in response to fluid forces and collisions. The extent of platelet aggregation was measured by absorption spectroscopy using the Beer–Lambert equation.

 

MissingLinkText

Conclusion

Platelets play an important role in hemostasis and thrombus formation. Recent progress in computer technology and mathematical modeling has enabled the reconstruction of various biological functions of platelets based on simple physical principles. The validity of these mathematical models was confirmed through detailed quantitative biological experiments. The future progress of “theoretical medicine,” starting from simple physical principles to understanding complicated biomedical phenomena, is expected in platelet biology. Theoretically, it is important to address the enormous heterogeneity of biological phenomena that occur at scales such as molecules, cells, tissues/organs, and the human body.

 

MissingLinkText

 

MissingLinkText

Conflict of Interest

Shinya Goto received a modest personal fee from Amgen, Merck Sharp and Dohme (MSD), Jansen Pharma, and Antos Therapeutics. S.G. received honoraria from the American Heart Association for serving as an Associate Editor for Circulation, and from Duke University and Harvard University for serving as a Steering Committee Member for Clinical Trials.

• References

• 1 Goto S, Hasebe T, Takagi S. Platelets: small in size but essential in the regulation of vascular homeostasis—translation from basic science to clinical medicine. Circ J 2015; 79 (09) 1871-1881
• 2 Italiano Jr JE, Bergmeier W, Tiwari S. et al. Mechanisms and implications of platelet discoid shape. Blood 2003; 101 (12) 4789-4796
• 3 Frojmovic MM, Milton JG. Human platelet size, shape, and related functions in health and disease. Physiol Rev 1982; 62 (01) 185-261
• 4 Goto S. Understanding the mechanism of platelet thrombus formation under blood flow conditions and the effect of new antiplatelet agents. Curr Vasc Pharmacol 2004; 2 (01) 23-32
• 5 Versteeg HH, Heemskerk JW, Levi M, Reitsma PH. New fundamentals in hemostasis. Physiol Rev 2013; 93 (01) 327-358
• 6 Scridon A. Platelets and their role in hemostasis and thrombosis—from physiology to pathophysiology and therapeutic implications. Int J Mol Sci 2022; 23 (21) 12772
• 7 Smyth SS, McEver RP, Weyrich AS. et al; 2009 Platelet Colloquium Participants. Platelet functions beyond hemostasis. J Thromb Haemost 2009; 7 (11) 1759-1766
• 8 Sachs L, Denker C, Greinacher A, Palankar R. Quantifying single-platelet biomechanics: an outsider's guide to biophysical methods and recent advances. Res Pract Thromb Haemost 2020; 4 (03) 386-401
• 9 Bergal HT, Jiang Y, Yang D, Springer TA, Wong WP. Conformation of von Willebrand factor in shear flow revealed with stroboscopic single-molecule imaging. Blood 2022; 140 (23) 2490-2499
• 10 Thomas MR, Storey RF. The role of platelets in inflammation. Thromb Haemost 2015; 114 (03) 449-458
• 11 Gawaz M, Langer H, May AE. Platelets in inflammation and atherogenesis. J Clin Invest 2005; 115 (12) 3378-3384
• 12 Koupenova M, Clancy L, Corkrey HA, Freedman JE. Circulating platelets as mediators of immunity, inflammation, and thrombosis. Circ Res 2018; 122 (02) 337-351
• 13 Hagihara M, Higuchi A, Tamura N. et al. Platelets, after exposure to a high shear stress, induce IL-10-producing, mature dendritic cells in vitro. J Immunol 2004; 172 (09) 5297-5303
• 14 Goto S, Ichikawa N, Lee M. et al. Platelet surface P-selectin molecules increased after exposing platelet to a high shear flow. Int Angiol 2000; 19 (02) 147-151
• 15 Tamura N, Yoshida M, Ichikawa N. et al. Shear-induced von Willebrand factor-mediated platelet surface translocation of the CD40 ligand. Thromb Res 2002; 108 (5-6): 311-315
• 16 Danese S, Fiocchi C. Platelet activation and the CD40/CD40 ligand pathway: mechanisms and implications for human disease. Crit Rev Immunol 2005; 25 (02) 103-121
• 17 Freedman JE. CD40-CD40L and platelet function: beyond hemostasis. Circ Res 2003; 92 (09) 944-946
• 18 Zaid Y, Merhi Y. Implication of platelets in immuno-thrombosis and thrombo-inflammation. Front Cardiovasc Med 2022; 9: 863846
• 19 Goto S. Propagation of arterial thrombi: local and remote contributory factors. Arterioscler Thromb Vasc Biol 2004; 24 (12) 2207-2208
• 20 Popel AS, Johnson PC. Microcirculation and hemorheology. Annu Rev Fluid Mech 2005; 37: 43-69
• 21 Kawamura Y, Takahari Y, Tamura N. et al. Imaging of structural changes in endothelial cells and thrombus formation at the site of FeCl(3)-induced injuries in mice cremasteric arteries. J Atheroscler Thromb 2009; 16 (06) 807-814
• 22 André P, Denis CV, Ware J. et al. Platelets adhere to and translocate on von Willebrand factor presented by endothelium in stimulated veins. Blood 2000; 96 (10) 3322-3328
• 23 Lindqvist T, Fahraeus R. The viscosity of the blood in narrow capillary tubes. Am J Physiol-Legacy Content 1931; 96: 562-568
• 24 Herczyński R. Fåhræus effect revisited. Arch Mech 2016; 68 (01) 81-93
• 25 Taylor M, Robertson JS. The flow of blood in narrow tubes. I. A capillary microphotometer: an apparatus for measuring the optical density of flowing blood. Aust J Exp Biol Med Sci 1954; 32 (05) 721-732
• 26 Ii S, Sugiyama K, Takagi S. et al. A computational blood flow analysis in a capillary vessel including multiple red blood cells and platelets. J Biomech Sci Engrg 2012; 7(1): 72-83
• 27 Tamura N, Shimizu K, Shiozaki S. et al. Important regulatory roles of erythrocytes in platelet adhesion to the von Willebrand factor on the wall under blood flow conditions. Thromb Haemost 2022; 122 (06) 974-983
• 28 Ruggeri ZM, Mendolicchio GL. Adhesion mechanisms in platelet function. Circ Res 2007; 100 (12) 1673-1685
• 29 Goto S, Salomon DR, Ikeda Y, Ruggeri ZM. Characterization of the unique mechanism mediating the shear-dependent binding of soluble von Willebrand factor to platelets. J Biol Chem 1995; 270 (40) 23352-23361
• 30 Vogel B, Claessen BE, Arnold SV. et al. ST-segment elevation myocardial infarction. Nat Rev Dis Primers 2019; 5 (01) 39
• 31 Goto S, Ikeda Y, Saldívar E, Ruggeri ZM. Distinct mechanisms of platelet aggregation as a consequence of different shearing flow conditions. J Clin Invest 1998; 101 (02) 479-486
• 32 Ruggeri ZM. von Willebrand factor. J Clin Invest 1997; 99 (04) 559-564
• 33 McGrath RT, McRae E, Smith OP, O'Donnell JS. Platelet von Willebrand factor—structure, function and biological importance. Br J Haematol 2010; 148 (06) 834-843
• 34 Wagner DD. The Weibel-Palade body: the storage granule for von Willebrand factor and P-selectin. Thromb Haemost 1993; 70 (01) 105-110
• 35 Jones TR, Kao KJ, Pizzo SV, Bigner DD. Endothelial cell surface expression and binding of factor VIII/von Willebrand factor. Am J Pathol 1981; 103 (02) 304-308
• 36 Zanetta L, Marcus SG, Vasile J. et al. Expression of Von Willebrand factor, an endothelial cell marker, is up-regulated by angiogenesis factors: a potential method for objective assessment of tumor angiogenesis. Int J Cancer 2000; 85 (02) 281-288
• 37 Rand JH, Glanville RW, Wu X-X. et al. The significance of subendothelial von Willebrand factor. Thromb Haemost 1997; 78 (01) 445-450
• 38 Houdijk WP, de Groot PG, Nievelstein PF, Sakariassen KS, Sixma JJ. Subendothelial proteins and platelet adhesion. von Willebrand factor and fibronectin, not thrombospondin, are involved in platelet adhesion to extracellular matrix of human vascular endothelial cells. Arteriosclerosis 1986; 6 (01) 24-33
• 39 Nieswandt B, Brakebusch C, Bergmeier W. et al. Glycoprotein VI but not α2β1 integrin is essential for platelet interaction with collagen. EMBO J 2001; 20 (09) 2120-2130
• 40 Pareti FI, Fujimura Y, Dent JA, Holland LZ, Zimmerman TS, Ruggeri ZM. Isolation and characterization of a collagen binding domain in human von Willebrand factor. J Biol Chem 1986; 261 (32) 15310-15315
• 41 Shiozaki S, Ishikawa KL, Takagi S. Numerical study on platelet adhesion to vessel walls using the kinetic Monte Carlo method. Journal of Biomechanical Science and Engineering 2012; 7: 275-283
• 42 Shiozaki S, Takagi S, Goto S. Prediction of molecular interaction between platelet glycoprotein Ibα and von Willebrand factor using molecular dynamics simulations. J Atheroscler Thromb 2016; 23 (04) 455-464
• 43 Kim J, Zhang C-Z, Zhang X, Springer TA. A mechanically stabilized receptor-ligand flex-bond important in the vasculature. Nature 2010; 466 (7309) 992-995
• 44 Tobimatsu H, Nishibuchi Y, Sudo R, Goto S, Tanishita K. Adhesive forces between A1 domain of von Willebrand factor and N-terminus domain of glycoprotein Ibα measured by atomic force microscopy. J Atheroscler Thromb 2015; 22 (10) 1091-1099
• 45 Wang Y, Li Y, Zhang S. et al. Friction between a single platelet and fibrinogen. Friction 2024; 12: 2344-2354
• 46 Nakayama M, Goto S, Goto S. Effects of caplacizumab, a specific inhibitor of the A1 domain of von Willebrand factor binding with platelet membrane glycoprotein (GP) Ibα, on the length of platelet pseudopods supporting platelet adhesions on immobilized von Willebrand factor under blood flow condition. J Biorheol 2022; 36(2): 68-75
• 47 Savage B, Saldívar E, Ruggeri ZM. Initiation of platelet adhesion by arrest onto fibrinogen or translocation on von Willebrand factor. Cell 1996; 84 (02) 289-297
• 48 Brooks BR, Brooks III CL, Mackerell Jr AD. et al. CHARMM: the biomolecular simulation program. J Comput Chem 2009; 30 (10) 1545-1614
• 49 Brooks BR, Bruccoleri RE, Olafson BD. et al. CHARMM: a program for macromolecular energy, minimization, and dynamics calculations. J Comput Chem 1983; 4: 187-217
• 50 Zhu X, Lopes PE, Mackerell Jr AD. Recent developments and applications of the CHARMM force fields. Wiley Interdiscip Rev Comput Mol Sci 2012; 2 (01) 167-185
• 51 Pastor RW, Mackerell Jr AD. Development of the CHARMM force field for lipids. J Phys Chem Lett 2011; 2 (13) 1526-1532
• 52 Ruedenberg K. The physical nature of the chemical bond. Rev Mod Phys 1962; 34: 326
• 53 Goto S, Oka H, Ayabe K. et al. Prediction of binding characteristics between von Willebrand factor and platelet glycoprotein Ibα with various mutations by molecular dynamic simulation. Thromb Res 2019; 184: 129-135
• 54 Wang P, Sheriff J, Zhang P, Deng Y, Bluestein D. A multiscale model for shear-mediated platelet adhesion dynamics: correlating in silico with in vitro results. Ann Biomed Eng 2023; 51 (05) 1094-1105
• 55 Garcia-Cantu E, Spaulding C, Corcos T. et al. Stent implantation in acute myocardial infarction. Am J Cardiol 1996; 77 (07) 451-454
• 56 Grines CL, Cox DA, Stone GW. et al; Stent Primary Angioplasty in Myocardial Infarction Study Group. Coronary angioplasty with or without stent implantation for acute myocardial infarction. N Engl J Med 1999; 341 (26) 1949-1956
• 57 Stone GW, Lansky AJ, Pocock SJ. et al; HORIZONS-AMI Trial Investigators. Paclitaxel-eluting stents versus bare-metal stents in acute myocardial infarction. N Engl J Med 2009; 360 (19) 1946-1959
• 58 Spaulding C, Henry P, Teiger E. et al; TYPHOON Investigators. Sirolimus-eluting versus uncoated stents in acute myocardial infarction. N Engl J Med 2006; 355 (11) 1093-1104
• 59 Eto K, Goto S, Shimazaki T. et al. Two distinct mechanisms are involved in stent thrombosis under flow conditions. Platelets 2001; 12 (04) 228-235
• 60 Sakakibara M, Goto S, Eto K, Tamura N, Isshiki T, Handa S. Application of ex vivo flow chamber system for assessment of stent thrombosis. Arterioscler Thromb Vasc Biol 2002; 22 (08) 1360-1364
• 61 Tomita A, Tamura N, Nanazawa Y, Shiozaki S, Goto S. Development of virtual platelets implementing the functions of three platelet membrane proteins with different adhesive characteristics. J Atheroscler Thromb 2015; 22 (02) 201-210
• 62 Leiderman K, Fogelson AL. Grow with the flow: a spatial-temporal model of platelet deposition and blood coagulation under flow. Math Med Biol 2011; 28 (01) 47-84
• 63 Shi X, Yang J, Huang J. et al. Effects of different shear rates on the attachment and detachment of platelet thrombi. Mol Med Rep 2016; 13 (03) 2447-2456
• 64 Jen CJ, Li HM, Wang J-S, Chen HI, Usami S. Flow-induced detachment of adherent platelets from fibrinogen-coated surface. Am J Physiol 1996; 270 (1 Pt 2): H160-H166
• 65 Fogelson AL. A mathematical model and numerical method for studying platelet adhesion and aggregation during blood clotting. J Comput Phys 1984; 56: 111-134
• 66 Goto S, Tamura N, Eto K, Ikeda Y, Handa S. Functional significance of adenosine 5′-diphosphate receptor (P2Y(12)) in platelet activation initiated by binding of von Willebrand factor to platelet GP Ibalpha induced by conditions of high shear rate. Circulation 2002; 105 (21) 2531-2536
• 67 Zucker M, Nachmias V. Platelet activation. Arteriosclerosis 1985; 5: 2-18
• 68 Niiya K, Hodson E, Bader R. et al. Increased surface expression of the membrane glycoprotein IIb/IIIa complex induced by platelet activation. Relationship to the binding of fibrinogen and platelet aggregation. Blood 1987; 70 (02) 475-483
• 69 Shattil SJ, Hoxie JA, Cunningham M, Brass LF. Changes in the platelet membrane glycoprotein IIb.IIIa complex during platelet activation. J Biol Chem 1985; 260 (20) 11107-11114
• 70 Kroll MH, Schafer AI. Biochemical mechanisms of platelet activation. Blood 1989; 74 (04) 1181-1195
• 71 Hartwig JH. Mechanisms of actin rearrangements mediating platelet activation. J Cell Biol 1992; 118 (06) 1421-1442
• 72 Goto S, Tamura N, Ishida H, Ruggeri ZM. Dependence of platelet thrombus stability on sustained glycoprotein IIb/IIIa activation through adenosine 5′-diphosphate receptor stimulation and cyclic calcium signaling. J Am Coll Cardiol 2006; 47 (01) 155-162
• 73 Varga-Szabo D, Braun A, Nieswandt B. Calcium signaling in platelets. J Thromb Haemost 2009; 7 (07) 1057-1066
• 74 Rink TJ, Sage SO. Calcium signaling in human platelets. Annu Rev Physiol 1990; 52: 431-449
• 75 Kaibuchi K, Takai Y, Sawamura M, Hoshijima M, Fujikura T, Nishizuka Y. Synergistic functions of protein phosphorylation and calcium mobilization in platelet activation. J Biol Chem 1983; 258 (11) 6701-6704
• 76 Shattil SJ, Brugge JS. Protein tyrosine phosphorylation and the adhesive functions of platelets. Curr Opin Cell Biol 1991; 3 (05) 869-879
• 77 Nakayama M, Goto S, Goto S. Development of the integrated computer simulation model of the intracellular, transmembrane, and extracellular domain of platelet integrin α _IIb β ₃ (platelet membrane glycoprotein: GPIIb-IIIa). TH Open 2024; 8 (01) e96-e105
• 78 Calvete JJ. On the structure and function of platelet integrin α IIb β 3, the fibrinogen receptor. Proc Soc Exp Biol Med 1995; 208 (04) 346-360
• 79 Bennett JS. Platelet-fibrinogen interactions. Ann N Y Acad Sci 2001; 936: 340-354
• 80 Topol EJ, Byzova TV, Plow EF. Platelet GPIIb-IIIa blockers. Lancet 1999; 353 (9148) 227-231
• 81 Adair BD, Yeager M. Three-dimensional model of the human platelet integrin alpha IIbbeta 3 based on electron cryomicroscopy and x-ray crystallography. Proc Natl Acad Sci U S A 2002; 99 (22) 14059-14064
• 82 Xiao T, Takagi J, Coller BS, Wang JH, Springer TA. Structural basis for allostery in integrins and binding to fibrinogen-mimetic therapeutics. Nature 2004; 432 (7013) 59-67
• 83 Wegener KL, Partridge AW, Han J. et al. Structural basis of integrin activation by talin. Cell 2007; 128 (01) 171-182
• 84 Moser M, Nieswandt B, Ussar S, Pozgajova M, Fässler R. Kindlin-3 is essential for integrin activation and platelet aggregation. Nat Med 2008; 14 (03) 325-330
• 85 Galli M, Bevers EM, Comfurius P, Barbui T, Zwaal RF. Effect of antiphospholipid antibodies on procoagulant activity of activated platelets and platelet-derived microvesicles. Br J Haematol 1993; 83 (03) 466-472
• 86 Pasquet J-M, Toti F, Nurden AT, Dachary-Prigent J. Procoagulant activity and active calpain in platelet-derived microparticles. Thromb Res 1996; 82 (06) 509-522
• 87 Wood JP, Silveira JR, Maille NM, Haynes LM, Tracy PB. Prothrombin activation on the activated platelet surface optimizes expression of procoagulant activity. Blood 2011; 117 (05) 1710-1718
• 88 Bevers EM, Comfurius P, Zwaal RF. Platelet procoagulant activity: physiological significance and mechanisms of exposure. Blood Rev 1991; 5 (03) 146-154
• 89 Miyazaki Y, Nomura S, Miyake T. et al. High shear stress can initiate both platelet aggregation and shedding of procoagulant containing microparticles. Blood 1996; 88 (09) 3456-3464
• 90 Lentz BR. Exposure of platelet membrane phosphatidylserine regulates blood coagulation. Prog Lipid Res 2003; 42 (05) 423-438
• 91 Schoenwaelder SM, Yuan Y, Josefsson EC. et al. Two distinct pathways regulate platelet phosphatidylserine exposure and procoagulant function. Blood 2009; 114 (03) 663-666
• 92 van Kruchten R, Mattheij NJ, Saunders C. et al. Both TMEM16F-dependent and TMEM16F-independent pathways contribute to phosphatidylserine exposure in platelet apoptosis and platelet activation. Blood 2013; 121 (10) 1850-1857
• 93 Goto S, Tamura N, Li M. et al. Different effects of various anti-GPIIb-IIIa agents on shear-induced platelet activation and expression of procoagulant activity. J Thromb Haemost 2003; 1 (09) 2022-2030
• 94 Suzuki J, Umeda M, Sims PJ, Nagata S. Calcium-dependent phospholipid scrambling by TMEM16F. Nature 2010; 468 (7325) 834-838
• 95 Mizuno H, Fujimoto Z, Atoda H, Morita T. Crystal structure of an anticoagulant protein in complex with the Gla domain of factor X. Proc Natl Acad Sci U S A 2001; 98 (13) 7230-7234
• 96 Sunnerhagen M, Forsén S, Hoffrén A-M, Drakenberg T, Teleman O, Stenflo J. Structure of the Ca(2+)-free Gla domain sheds light on membrane binding of blood coagulation proteins. Nat Struct Biol 1995; 2 (06) 504-509
• 97 Stenflo J. Contributions of Gla and EGF-like domains to the function of vitamin K-dependent coagulation factors. Crit Rev Eukaryot Gene Expr 1999; 9 (01) 59-88
• 98 Huang M, Rigby AC, Morelli X. et al. Structural basis of membrane binding by Gla domains of vitamin K-dependent proteins. Nat Struct Biol 2003; 10 (09) 751-756
• 99 Majumder R, Quinn-Allen MA, Kane WH, Lentz BR. A phosphatidylserine binding site in factor Va C1 domain regulates both assembly and activity of the prothrombinase complex. Blood 2008; 112 (07) 2795-2802
• 100 Wang J, Yu C, Zhuang J. et al. The role of phosphatidylserine on the membrane in immunity and blood coagulation. Biomark Res 2022; 10 (01) 4
• 101 Spronk HM, ten Cate H, van der Meijden PE. Differential roles of tissue factor and phosphatidylserine in activation of coagulation. Thromb Res 2014; 133 (Suppl. 01) S54-S56
• 102 Goto S, Tamura N, Ayabe K. et al. A method and preliminary results of in silico computer simulation for the formation of mix thrombi with platelet and fibrin. Journal of Biorheology 2017; 31(2): 30-34
• 103 Born GVR. Aggregation of blood platelets by adenosine diphosphate and its reversal. Nature 1962; 194: 927-929
• 104 Jackson SP. The growing complexity of platelet aggregation. Blood 2007; 109 (12) 5087-5095
• 105 Kulkarni S, Dopheide SM, Yap CL. et al. A revised model of platelet aggregation. J Clin Invest 2000; 105 (06) 783-791
• 106 Goto S, Sakai H, Goto M. et al. Enhanced shear-induced platelet aggregation in acute myocardial infarction. Circulation 1999; 99 (05) 608-613
• 107 Ikeda Y, Handa M, Kawano K. et al. The role of von Willebrand factor and fibrinogen in platelet aggregation under varying shear stress. J Clin Invest 1991; 87 (04) 1234-1240
• 108 Goto S, Ikeda Y, Murata M. et al. Epinephrine augments von Willebrand factor-dependent shear-induced platelet aggregation. Circulation 1992; 86 (06) 1859-1863

Publication History

Received: 31 March 2025

Accepted: 18 July 2025

Accepted Manuscript online:
05 August 2025

Article published online:
20 August 2025