Scaling aspects of lymphocyte trafficking.

We consider the long lived pool of B and T cells that recirculate through blood, tissues and the lymphatic system of an animal with body mass M. We derive scaling rules (allometric relations) for: (1) the rate of production of mature lymphocytes, (2) the accumulation of lymphocytes in the tissues, (3) the flux of lymphocytes through the lymphatic system, (4) the number of lymph nodes, (5) the number of lymphocytes per clone within a lymph node, and (6) the total number of lymphocytes within a lymph node. Mass-dependent aspects of immune learning and of the immunological self are shown to be not very significant.

A simple theory of peptide interactions on a membrane surface: excluded volume and entropic order.

A simple theory of the interactions of peptides bound onto a lipid membrane is developed, modeling the peptides as rods on a surface. At low peptide surface-concentration, excluded volume dominates the peptide-peptide interactions and the orientation of the peptides is random, resulting in an isotropic configuration. However, at high peptide density on the membrane, the peptides become orientationally ordered, resulting in an anisotropic configuration.

Some scaling principles for the immune system.

Using recent progress in biological scaling, we explore the way in which the immune system of an animal scales with its mass (M). It is shown that the number of cells in a single clone of B cells should scale as M and that the B-cell repertoire scales as ln (cM), where c is a constant. The time that a B cell needs to circulate once through the organism is shown to scale as M(1/4)ln (cM).

Kinetics of ligand binding to a cluster of membrane-associated receptors.

The process of ligand binding to a cluster of membrane-associated receptors is examined theoretically. The theoretical model proposed involves the diffusion of ligands from the solution to the disc-like cluster of receptors on the surface of the spherical cell. When the ligand hits the internal part of the disc-like cluster, it begins to move laterally until it leaves the disc through its outer surface or is bound by one of the receptors inside the disc.

Chemoreception by a cell with age-dependent receptor binding sites.

The authors determine the time-dependent ligand current into a spherical cell that is covered with a large number of age-dependent receptors. These receptors can be in either of two states: active (i.e.