Cell Models and the Homeostasis Problem

Abstract

In mammalian cells initiation of DNA replication requires RNA synthesis in the early G₁ — phase and synthesis of an inducer during the S — phase. The mitotic operon may be switched on and off by an operonic trigger which in turn is based upon the mitotic operon and the histospecific operon. The assumption of a block of the two operon activities during the S — phase guarantees the oscillatory action of the trigger. The model contains the feedback with the total cell number via the repressor for the histospecific operon. Taking into account a competition for micromolecular precursors between the processes implied in protein synthesis and enzymatic reactions, a single micromolecular precursor for protein synthesis suffices which is synthesized under the control of an enzyme (as far as steady state can be assumed) and for whose decay a lytic enzyme is required in addition. The amount of gene activation is determined by the switching states of certain triggers. For all-or-none triggers one may adopt binary (logical) functions (2). The gene activities which enable the different kinds of work done by stem cells (low proliferation), immature cells (high proliferation), mature cells (high histospecificity) and dying cells, can be obtained by a system of triggers. In the model of cell cycle the cell volume must be included, too. The initiation of DNA replication can be considered as due to accumulation of a threshold membrane substance. The feedback between growth rate and the numbers of i-type cells (i.e. stem-immature-, mature or dying cells) can be considered as following (3) with intercellular diffusion of the chalone. A pair of equations is obtained which describes: 1. the intra-extra-cellular exchange of chalones for cells of this type and 2. the balance of the extracellular chalone being subject to a decay of certain rate. The model neglects many aspects of cell regulation. However, since DNA transription is the first amplifying cascade in the sequence of DNA → RNA → enzyme → enzymatic reaction the consideration of gene activation control can be regarded only as a first approximation which must be elaborated further.