Bifurcation and singularity analysis of a molecular network for the induction of long-term memory.

Withdrawal reflexes of the mollusk Aplysia exhibit sensitization, a simple form of long-term memory (LTM). Sensitization is due, in part, to long-term facilitation (LTF) of sensorimotor neuron synapses. LTF is induced by the modulatory actions of serotonin (5-HT). Pettigrew et al. developed a computational model of the nonlinear intracellular signaling and gene network that underlies the induction of 5-HT-induced LTF. The model simulated empirical observations that repeated applications of 5-HT induce persistent activation of protein kinase A (PKA) and that this persistent activation requires a suprathreshold exposure of 5-HT. This study extends the analysis of the Pettigrew model by applying bifurcation analysis, singularity theory, and numerical simulation. Using singularity theory, classification diagrams of parameter space were constructed, identifying regions with qualitatively different steady-state behaviors. The graphical representation of these regions illustrates the robustness of these regions to changes in model parameters. Because persistent protein kinase A (PKA) activity correlates with Aplysia LTM, the analysis focuses on a positive feedback loop in the model that tends to maintain PKA activity. In this loop, PKA phosphorylates a transcription factor (TF-1), thereby increasing the expression of an ubiquitin hydrolase (Ap-Uch). Ap-Uch then acts to increase PKA activity, closing the loop. This positive feedback loop manifests multiple, coexisting steady states, or multiplicity, which provides a mechanism for a bistable switch in PKA activity. After the removal of 5-HT, the PKA activity either returns to its basal level (reversible switch) or remains at a high level (irreversible switch). Such an irreversible switch might be a mechanism that contributes to the persistence of LTM. The classification diagrams also identify parameters and processes that might be manipulated, perhaps pharmacologically, to enhance the induction of memory. Rational drug design, to affect complex processes such as memory formation, can benefit from this type of analysis.

Long-term synaptic facilitation of tail sensorimotor connections in {\it Aplysia\/}

Long-term sensitization in Aplysia is a well studied model for the examination of the cellular and molecules mechanisms of long-term memory. Several lines of evidence suggest long-term sensitization is mediated at least partially by long-term synaptic facilitation between the sensory and motor neurons. The sensitization training and one of its analogues, serotonin (5-HT), can induce long-term facilitation. In this study, another analogue to long-term sensitization training has been developed. Stimulation of peripheral nerves of pleural-pedal ganglia preparation induced long-term facilitation at both 24 hr and 48 hr. This is the first report that long-term facilitation in Aplysia persists for more than 24 hr, which is consistent with the observation that long-term sensitization lasts for more than one day. Thus, the data support the hypothesis that long-term facilitation is an important mechanism for long-term sensitization.^ One of the major differences between short-term and long-term facilitation is that long-term facilitation requires protein synthesis. Therefore, the effects of anisomycin, a protein synthesis inhibitor, on long-term facilitation was examined. Long-term facilitation induced by nerve stimulation was inhibited by 2 $\mu$M anisomycin, which inhibits $\sim$90% of protein synthesis. Nevertheless, at higher concentration (20 $\mu$M), anisomycin induced long-term facilitation by itself, which raises an interesting question about the function of anisomycin other than protein synthesis inhibition.^ Since protein synthesis is critical for long-term facilitation, a major goal is to identify and functionally characterize the molecules whose mRNA levels are altered during the formation of long-term facilitation. Behavioral training or its analogues (nerve stimulation and 5-HT) increases the level of mRNA of calmodulin (CaM). Thus, the role of Ca$\sp{2+}$-CaM-dependent protein kinase II (CaMKII), a major substrate of CaM, in long-term facilitation induced by nerve stimulation was examined. KN-62, a specific CaMKII inhibitor, did not block either the induction or the maintenance of long-term facilitation induced by nerve stimulation. These data indicate that CaMKII may not be involved in long-term facilitation. Another protein whose mRNA level of a molecule was increased by the behavioral training and the treatment of 5-HT is Aplysia tolloid/BMP-1-like protein 1 (apTBL-1). Tolloid in Drosophila and BMP-1 in human tissues are believed to be secreted as a metalloprotease to activate TGF-$\beta.$ Thus, the long-term effects of recombinant human TGF-$\beta1$ on synaptic strength were examined. Treatment of ganglia with TGF-$\beta1$ produced long-term facilitation, but not short-term or intermediate-term facilitation ($\le$4 hr). In addition, TGF-$\beta1$ and 5-HT were not additive in producing long-term facilitation, which indicates an interaction between two cascades. Moreover, 5-HT-induced facilitation (at both 24 hr and 48 hr) and nerve stimulation-induced facilitation (at 24 hr) were inhibited by TGF-$\beta$ sRII, a TGF-$\beta$ inhibitor. These results suggest that TGF-$\beta$ is part of the cascade of events underlying long-term sensitization, and also indicate that a signaling molecule used in development may also have functions in adult neuronal plasticity. ^