Fluctuations of cell population in a colonic crypt.

The number of stem cells in a colonic crypt is often very small, which leads to large intrinsic fluctuations in the cell population. Based on the model of cell population dynamics with linear feedback in a colonic crypt, we present a stochastic dynamics of the cell population [including stem cells (SCs), transit amplifying cells (TACs), and fully differentiated cells (FDCs)]. The Fano factor, covariance, and susceptibility formulas of the cell population around the steady state are derived by using the Langevin theory. In the range of physiologically reasonable parameter values, it is found that the stationary populations of TACs and FDCs exhibit an approximately threshold behavior as a function of the net growth rate of TACs, and the reproductions of TACs and FDCs can be classified into three regimens: controlled, crossover, and uncontrolled. With the increasing of the net growth rate of TACs, there is a maximum of the relative intrinsic fluctuations (i.e., the Fano factors) of TACs and FDCs in the crossover region. For a fixed differentiation rate and the net growth rate of SCs, the covariance of fluctuations between SCs and TACs has a maximum in the crossover region. However, the susceptibilities of both TACs and FDCs to the net growth rate of TACs have a minimum in the crossover region.

Effects of inositol 1,4,5-trisphosphate receptor-mediated intracellular stochastic calcium oscillations on activation of glycogen phosphorylase.

In various cell types cytosolic calcium (Ca(2+)) is an important regulator. The possible role of Ca(2+) release from the inositol 1,4,5-trisphosphate (IP(3)) receptor channel in the regulation of the phosphorylation-dephosphorylation cycle process involved in glycogen degradation by glycogen phosphorylase have theoretically investigated by using the Li-Rinzel model for cytosolic Ca(2+) oscillations. For the case of deterministic cytosolic Ca(2+) oscillations, there exists an optimal frequency of cytosolic Ca(2+) oscillations at which the average fraction of active glycogen phosphorylase reaches a maximum value, and a mutation for the average fraction of active glycogen phosphorylase occurs at the higher bifurcation point of Ca(2+) oscillations. For the case of stochastic cytosolic Ca(2+) oscillations, the fraction of active phosphorylase is strongly affected by the number of IP(3) receptor channels and the level of IP(3) concentration. Small number of IP(3) receptor channels can potentiate the sensitivity of the activity of glycogen phosphorylase. The average frequency and amplitude of active phosphorylase stochastic oscillations are increased with the level of increasing IP(3) stimuli. The various distributions for the amplitude of active glycogen phosphorylase oscillations in parameters plane are discussed.

A theoretical study of effects of cytosolic Ca2+ oscillations on activation of glycogen phosphorylase.

Taking into account the Ca(2+)-stimulated degradation of inositol 1,4,5-trisphosphate (IP(3)) by a 3-kinase, we have theoretically explored the effects of both simple and complex Ca(2+) oscillations on the regulation of a phosphorylation-dephosphorylation cycle process involved in glycogen degradation by glycogen phosphorylase a-form, respectively. For the case of simple Ca(2+) oscillations, the roles of cytosolic Ca(2+) oscillations in the regulation of active phosphorylase depend upon the maximum rate of IP(3) degradation by the 3-kinase, V(M5). In particular, the smaller the values of V(M5) are, the lower the effective Ca(2+) threshold for the activation of glycogen phosphorylase will be. For the case of complex Ca(2+) oscillations, the average level of fraction of active phosphorylase is nearly independent from the level of stimulation increasing in the bursting oscillatory domain. Both simple and complex Ca(2+) oscillations can contribute to increase the efficiency and specificity of cellular signalling, and some theoretical results of activation of glycogen phosphorylase regulated by Ca(2+) oscillations are close to the experimental results for gene expression in lymphocytes.