Stochasticity and bifurcations in a reduced model with interlinked positive and negative feedback loops of CREB1 and CREB2 stimulated by 5-HT.

The cyclic AMP (cAMP)-response element-binding protein (CREB) family of transcription factors is crucial in regulating gene expression required for long-term memory (LTM) formation. Upon exposure of sensory neurons to the neurotransmitter serotonin (5-HT), CREB1 is activated via activation of the protein kinase A (PKA) intracellular signaling pathways, and CREB2 as a transcriptional repressor is relieved possibly via phosphorylation of CREB2 by mitogen-activated protein kinase (MAPK). Song et al. [18] proposed a minimal model with only interlinked positive and negative feedback loops of transcriptional regulation by the activator CREB1 and the repressor CREB2. Without considering feedbacks between the CREB proteins, Pettigrew et al. [8] developed a computational model characterizing complex dynamics of biochemical pathways downstream of 5-HT receptors. In this work, to describe more simply the biochemical pathways and gene regulation underlying 5-HT-induced LTM, we add the important extracellular sensitizing stimulus 5-HT as well as the product Ap-uch into the Song's minimal model. We also strive to examine dynamical properties of the gene regulatory network under the changing concentration of the stimulus, [5-HT], cooperating with the varying positive feedback strength in inducing a high state of CREB1 for the establishment of long-term memory. Different dynamics including monostability, bistability and multistability due to coexistence of stable steady states and oscillations is investigated by means of codimension-2 bifurcation analysis. At the different positive feedback strengths, comparative analysis of deterministic and stochastic dynamics reveals that codimension-1 bifurcation with respect to [5-HT] as the parameter can predict diverse stochastic behaviors resulted from the finite number of molecules, and the number of CREB1 molecules more and more preferentially resides near the high steady state with increasing [5-HT], which contributes to long-term memory formation.