Binding of platelets to VWF modeled as a function of platelet count and multimer length. The fractional occupancy of platelet binding sites on VWF multimers was calculated from the K_d for platelet GPIbα-A1 domain binding (∼4 μmol/L),^25,–27  plasma VWF concentration (∼10 μg/mL), VWF subunit mass (∼250 kDa), and number of GPIbα per platelet (∼28 000).²⁶  The probability that a multimer has bound a particular number x of platelets is given by the binomial formula for P(x,n), where n is the number of VWF A1 domains (or subunits) per multimer and y is the fractional occupancy of VWF domain A1 sites by GPIbα ([GPIbα-A1]/[A1]_total): P(0,n) = (1 − y)ⁿ and P(1,n) = ny(1 − y)ⁿ⁻¹. Therefore, the probability of having at least 1 platelet bound per multimer is 1 − (1 − y)ⁿ, and the probability of finding at least 2 platelets bound per multimer is 1 − {(1 − y)ⁿ + ny(1 − y)ⁿ⁻¹}. At a fixed multimer length (n = 20 subunits), P is greater than or equal to 2 platelets/multimer increases exponentially with increasing platelet count (A), whereas P is greater than or equal to 1 platelet/multimer increases approximately linearly with increasing platelet count (B). At a fixed platelet count (250 000/μL), P is greater than or equal to 2 platelets/multimer increases exponentially with increasing multimer length (C), whereas P is greater than or equal to 1 platelet/multimer increases approximately linearly with increasing multimer length (D).