The equilibrium size distribution of rouleaux

Abstract

Rouleaux are formed by the aggregation of red blood cells in the presence of macromolecules that bridge the membranes of adherent erythrocytes. We compute the size and degree of branching of rouleaux for macroscopic systems in thermal equilibrium in the absence of fluid flow. Using techniques from statistical mechanics, analytical expressions are derived for (a) the average number of rouleaux consisting of n cells and having m branch points; (b) the average number of cells per rouleau; (c) the average number of branch points per rouleau; and (d) the number of rouleaux with n cells, n = 1, 2, ..., in a system containing a total of N cells. We also present the results of numerical evaluations to establish the validity of asymptotic expressions that simplify our formal analytic results.

Evaluating the B-cell density with various activation functions using White Noise Path Integral Approach

“…The shape space is a conceptual and computational framework to view antibody-antigen affinity and its resultant consequences. It is a linear space of all possible sequences of S 1 , S 2 , S 3 , ….. S n , such that, each antibody is characterized by a specific point in S, which is called the shape [1]. The immune response phenomenon is modeled by the Brownian motion or diffusion in shape space.…”

“…There are interesting examples, like the trypanosomes causing African sleeping sickness [11], and the HIV virus [12,14] in which the organisms have the ability to change their surface proteins (antigens). Previous modeling of Perelson et al have the following assumptions for the mutation of antigens [1].…”

“…Within the germinal centers, the location in the body in which most somatic mutation occurs, dividing the B cells appear to be programmed to die [1]. However, they are rescued from dying in an affinitydependent fashion.…”

“…[7]), and polymer science [8,9] among others. 1 To whom any correspondence should be addressed. This study presents calculation of the B-cell density or the number of B-cells per volume using White Noise analysis.…”

“…The B-cell density represents the population of B-cells at a certain time after it has encountered foreign pathogens. We use as a starting point the model and design principles for immune system recognition done by Perelson and Wiegel [1].…”