Fluctuation and noise propagation in phenotypic transition cascades of clonal populations.

Quantitative modeling of fluctuations of each phenotype is a crucial step towards a fundamental understanding of noise propagation through various phenotypic transition cascades. The theoretical formulas for noise propagation in various phenotypic transition cascades are derived by using the linear noise approximation of master equation and the logarithmic gain. By virtue of the theoretical formulas, we study the noise propagation in bidirectional and unidirectional phenotypic transition cascades, respectively. It is found that noise propagation in these two phenotypic transition cascades evidently differs: In the bidirectional cascade, a systemic random environment is provided by a correlated global component. The total noise of each phenotype is mainly determined by the intrinsic noise and the transmitted noise from other phenotypes. The intrinsic noise enlarged by interconversion through an added part shows a novel noise propagation mechanism. However, in the unidirectional cascade, the random environment of each downstream phenotype is provided by upstream phenotypes. The total noise of each downstream phenotype is mainly determined by the transmitted noises from upstream phenotypes. The intrinsic noise and the conversion noise can propagate in both bidirectional and unidirectional phenotypic transition cascades.

[Ammonium Adsorption Characteristics in Aqueous Solution by Dairy Manure Biochar].

The adsorption characteristics of ammonium from aqueous solution onto biochar derived from dairy manure were investigated as a function of parameters such as solution pH, particle size, adsorbent dosage, temperature and competitive cations. The results indicated that the effects of other cations on the adsorption of ammonium followed the order of preference Na > Ca2+ at identical mass concentrations. It was observed that pH played an important role in the ammonium adsorption and the optimal pH values ranged between 5 and 8. The kinetic data fitted the pseudo-second-order model (R2 = 0.967 3) but showed very poor fits for the pseudo-first-order model (R2 = 0.765 9) and the Elovich model (R2 = 0.724 9). The results from the Intra-particle model also showed that there were two separate stages in sorption process, which were external diffusion and the diffusion of inter-particle. Adsorption isotherms for dairy manure biochar were fitted the Freundlich model (R2 = 0.976 2) more effectively than other models. Thermodynamics parameters such as free energy (ΔGθ), enthalpy (ΔHθ), and entropy (ΔSθ) were also determined, which indicated that the adsorption was a spontaneous and endothermic process.

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.