Analysis by Computer of some Oscillatory
Features of the Red Cell System
J. KIRK, and J. S. ORR
With 3 Figures
Abstract
The oscillatory nature of the red blood cell and bone marrow stem cell system,
which is composed of two interacting feedback control loops, is studied. A
mathematical description of the system is formulated as four simultaneous nonlinear difference-differential equations in four variables, and the constants derived
from a wide range of experimental data. The equations are evaluated numerically by
daily increments using a digital computer. The behaviour of the formulation is
compared with experimental data. Important features of the oscillations are
described, and the entrainment of the frequencies between the loops is discussed
from the point of view of the synchronisation of non-linear oscillators, in the
light of an analogy with electronic oscillatory systems.
Introduction
The oscillatory nature of the red blood cell system has been demonstrated
in several experimental studies; of which those of PORTEOUS and LAJTHA
[3], HULSE [1] and ORR et al. [2] are of particular interest. The system can
be broken down naturally into two interacting feedback control loops, as
shown in figure 1; the red cell loop in which bone marrow stem cells are
differentiated under the stimulus of erythropoietin to form reticulocytes and
ultimately mature red cells, and the stem cell loop in which stem cells lost to
the differentiation channels are replenished by mitosis, controlled by the
stem cell specific mitotic inhibitor, chalone. Erythropoietin and chalone
are catabolized in proportion to their own level, and mature red cells disappear from the system after a fairly well defined lifetime. Erythropoietin
production is dependent on the reciprocal of a high power of the size of
the red cell population, while chalone production is proportional to the
stem cell population. The reticulocyte fraction of the red cell population
depends on the lifetime of a reticulocyte before becoming a mature red cell.
Other differentiation channels are considered as a constant drain on the
stem cell population.
15*
Features of the Red Cell System
J. KIRK, and J. S. ORR
With 3 Figures
Abstract
The oscillatory nature of the red blood cell and bone marrow stem cell system,
which is composed of two interacting feedback control loops, is studied. A
mathematical description of the system is formulated as four simultaneous nonlinear difference-differential equations in four variables, and the constants derived
from a wide range of experimental data. The equations are evaluated numerically by
daily increments using a digital computer. The behaviour of the formulation is
compared with experimental data. Important features of the oscillations are
described, and the entrainment of the frequencies between the loops is discussed
from the point of view of the synchronisation of non-linear oscillators, in the
light of an analogy with electronic oscillatory systems.
Introduction
The oscillatory nature of the red blood cell system has been demonstrated
in several experimental studies; of which those of PORTEOUS and LAJTHA
[3], HULSE [1] and ORR et al. [2] are of particular interest. The system can
be broken down naturally into two interacting feedback control loops, as
shown in figure 1; the red cell loop in which bone marrow stem cells are
differentiated under the stimulus of erythropoietin to form reticulocytes and
ultimately mature red cells, and the stem cell loop in which stem cells lost to
the differentiation channels are replenished by mitosis, controlled by the
stem cell specific mitotic inhibitor, chalone. Erythropoietin and chalone
are catabolized in proportion to their own level, and mature red cells disappear from the system after a fairly well defined lifetime. Erythropoietin
production is dependent on the reciprocal of a high power of the size of
the red cell population, while chalone production is proportional to the
stem cell population. The reticulocyte fraction of the red cell population
depends on the lifetime of a reticulocyte before becoming a mature red cell.
Other differentiation channels are considered as a constant drain on the
stem cell population.
15*