Statistical synthesis of osmotic fragility curves 1

Abstract

A mathematical–statistical model is derived whereby one may indirectly generate a frequency distribution of a variable, Y, by (1) defining a relationship between Y and variables, ${\mathit{X}}_{\mathit{i}}$ , upon which Y depends, (2) randomly generating values in the distributions (assumed normal) of ${\mathit{X}}_{\mathit{i}}$ and (3) solving for Y via the defining relation for each set of randomly generated ${\mathit{X}}_{\mathit{i}}$ . The model is used to synthesize red blood cell (RBC) osmotic fragility curves where Y is the hemolytic concentration and the ${\mathit{X}}_{\mathit{i}}$ are initial RBC volume, RBC membrane area at hemolysis, osmotically active fraction, pre-lytic K⁺ leak and membrane tension at hemolysis. Utilizing estimates of the latter five variables from the literature, the theoretical osmotic fragility curves obtained provide an excellent representation of osmotic fragility curves from the literature, as judged by least-squares criteria. Further, when literature values of the most reliably measured variables—initial volume and osmotically active fraction—are used in fitting theoretical to experimental osmotic fragility curves, the model serves to set limits on the three less reliably measured variables which will serve to guide further experimental work.