A mathematical model of B lymphocyte differentiation: Control by antigen

Abstract

A mathematical model of B lymphocyte differentiation, based on experimental results, has been developed. The model focuses on the role of antigen in initiating and regulating B cell differentiation while other mechanisms, acting in concert with antigen but the functioning of which can be circumvented under appropriate conditions, are not considered. The importance of presence of antigen at individual stages of B cell differentiation was studied in experiments with an easily metabolizable antigen. Immunocompetent cells (ICC), arising by antigen-independent differentiation of stem cells, are activated by antigen (they become immunologically activated cells--IAC). Excess of antigen drives IAC into the terminal stage (antibody-forming cells--AFC) thereby restricting proliferation. Exhaustive terminal differentiation results in tolerance. A low primary dose permits IAC to escape antigen; IAC proliferate and later give rise to resting memory cells (MC) which are amenable to reactivation. MC have higher avidity for antigen (due to higher affinity, number and density of receptors) and the effect of different doses of antigen on MC is diverse. A very low secondary dose induces tolerance, a medium dose secondary response, and the administration of a high dose of antigen also brings about tolerance. The model suggests that the fate of memory cells is controlled by the ratio R:Ag, of the number of immunoglobulin receptors on B cells (R) to the number of available antigenic molecules (Ag), low values R:Ag favouring stimulation to differentiation while high values of R:Ag favouring inactivation. A nonlinear system of ordinary differential equations, describing the development of the populations involved in antigen-driven B cell differentiation, was used to simulate experiments and good qualitative agreement was achieved.

Dynamical modelling of haematopoiesis: an integrated view over the system in homeostasis and under perturbation

“…The clinical importance of the haematopoietic system, as well as its privileged position as a model for stem cell biology, has inspired the development of mathematical models for more than three decades [12][13][14]. Since such a large system is not easily amenable to global modelling, most attempts have focused on specific aspects of the haematopoietic hierarchy in order to reduce complexity.…”

“…The tight control and regulation of all these concurrent processes are fundamental for maintenance of homeostasis as the system responds to external perturbations such as haemorrhage or disease by supplying the necessary number of mature blood cells. The clinical importance of the haematopoietic system, as well as its privileged position as a model for stem cell biology, has inspired the development of mathematical models for more than three decades [12][13][14]. Since such a large system is not easily amenable to global & 2012 The Author(s) Published by the Royal Society.…”

A Continuous Model of Three Scenarios of the Infection Process with Delayed Immune Response Factors

“…The main problem to analyze with the modified model is the issue of what scenarios are possible for spontaneous termination of an extreme process, that is, its transition to another quality after the phase of a rapid growth in virion number. The initial number of virions entering the body is thought to be important in certain situations [60]. The disease course may depend nonlinearly on the initial N(0) [61].…”

The use of gnotobiological models for the studies of immune mechanisms

“…The use of GF animals allows to distinguish conditions leading to low and high dose tolerance developed in pre-sensitized animals. Experimental data obtained by application of pre-formed Ag-Ab complexes and by antigenic stimulation of virgin immunocompetent cells or cells activated by antigen bearing increased number of specific receptors initiated construction of mathematical models [4]. It was proposed that ratio between cell receptors and number of antigen molecules decides if Ag-Ab complex will provide active membrane signal inducing cell response or an inhibitory, down regulatory signal similar to the target cells equipped with receptors for hormones.…”