The feed forward loop （FFL）, wherein a gene X can regulate target gene Z alone or cooperatively with gene Y, is one of the most important motifs in gene regulatory networks. Gene expression often involves a small number of reactant molecules and thus internal molecular fluctuation is considerable. Here we studied how an FFL responds to small external signal inputs at gene X, with particular attention paid to the fluctuation resonance （FR） phenomenon of gene Z. We found that for all coherent FFLs, where the sign of the direct regulation path from X to Z is the same as the overall sign of the indirect path via Y, the FR shows a regular single peak, while for incoherent FFLs, the FR exhibits distinct bimodal shapes. The results indicate that one could use small external signals to help identify the regulatory structure of an unknown FFL in complex gene networks.
The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only yields a steady state. Also,. the performance of such oscillations shows two maxima with the variation of the system size, indicating the occurrence of system size resonance. This behavior is found to be intimately connected with the canard phenomenon. Interestingly, it is also found that one of the optimal system sizes matches well with the real cell size, and such a match is robust to the variation of the control parameters.
