Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Sensory regulation of network components underlying ciliary locomotion in Hermissenda.

Ciliary locomotion in the nudibranch mollusk Hermissenda is modulated by the visual and graviceptive systems. Components of the neural network mediating ciliary locomotion have been identified including aggregates of polysensory interneurons that receive monosynaptic input from identified photoreceptors and efferent neurons that activate cilia. Illumination produces an inhibition of type I(i) (off-cell) spike activity, excitation of type I(e) (on-cell) spike activity, decreased spike activity in type III(i) inhibitory interneurons, and increased spike activity of ciliary efferent neurons. Here we show that pairs of type I(i) interneurons and pairs of type I(e) interneurons are electrically coupled. Neither electrical coupling or synaptic connections were observed between I(e) and I(i) interneurons. Coupling is effective in synchronizing dark-adapted spontaneous firing between pairs of I(e) and pairs of I(i) interneurons. Out-of-phase burst activity, occasionally observed in dark-adapted and light-adapted pairs of I(e) and I(i) interneurons, suggests that they receive synaptic input from a common presynaptic source or sources. Rhythmic activity is typically not a characteristic of dark-adapted, light-adapted, or light-evoked firing of type I interneurons. However, burst activity in I(e) and I(i) interneurons may be elicited by electrical stimulation of pedal nerves or generated at the offset of light. Our results indicate that type I interneurons can support the generation of both rhythmic activity and changes in tonic firing depending on sensory input. This suggests that the neural network supporting ciliary locomotion may be multifunctional. However, consistent with the nonmuscular and nonrhythmic characteristics of visually modulated ciliary locomotion, type I interneurons exhibit changes in tonic activity evoked by illumination.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.