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.

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.

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.

2-methylthio-N$\sp6$-dimethylallyl modification of adenosine 37 of tRNAs in {\it Escherichia coli\/} K-12

The hypermodified, hydrophobic 2-methylthio-N$\sp6$-(dimethylallyl)-adenosine (ms${2{\cdot}6}\atop1$A) residue occurs $3\sp\prime$ to the anticodon in tRNA species that read codons beginning with U. The first step (i$\sp6$A37 formation) of this modification is catalyzed by dimethylallyl diphosphate:tRNA dimethyallyltransferase (EC 2.5.1.8), which is the product of the miaA gene. Subsequent steps were proposed to be catalyzed by MiaB and MiaC enzymes to complete the ms${2{\cdot}6}\atop1$A37 modification. The study of functions of the ms${2{\cdot}6}\atop1$A37 is very important because this modified base is one of the best candidates for a role in global control in response to environmental stress. This dissertation describes the further delineation of functions of the ms${2{\cdot}6}\atop1$A37 modification in E. coli K-12 cells. This work provides significant information on functions of tRNA modifications in E. coli cells to adapt to stressful environmental conditions. Three hypotheses were tested in this work.^ The first hypothesis tested was that non-optimal translation processes cause increased spontaneous mutagenesis by the induction of SOS response in starving cells. To test this hypothesis, I measured spontaneous mutation rates of wild type cells and various mutant strains which are defective in tRNA modification, SOS response, or oxidative damage repair. I found that the miaA mutation acts as a mutator that increased Lac$\sp+$ reversion rates and Trp$\sp+$ reversion frequencies of the wild-type cells in starving conditions. However, the lexA3(Ind)(which abolishes the induction of SOS response) mutation abolished the mutator phenotype of the miaA mutant. The recA430 mutation, not other identified SOS genes, decreased the Lac$\sp+$ reversion to a less extent than that of the lexA3(Ind) mutation. These results suggest that RecA together with another unidentified SOS gene product are responsible for the process.^ The second hypothesis tested was that MiaA protein binds to full-length tRNA$\sp{\rm Phe}$ molecules in form of a protein dimer. To test this hypothesis, three versions of the MiaA protein and seven species of tRNA substrates were purified. Binding studies by gel mobility shift assays, filter binding assays and gel filtration shift assays support the hypothesis that MiaA protein binds to full-length tRNA$\sp{\rm Phe}$ as a protein dimer but as a monomer to the anticodon stem-and-loop. These results were further supported by using steady state enzyme kinetic studies.^ The third hypothesis tested in this work was that the miaB gene in E. coli exists and is clonable. The miaB::Tn10dCm insertion mutation of Salmonella typhimurium was transduced to E. coli K-12 cells by using P$\sb1$ and P$\sb{22}$ bacteriophages. The insertion was confirmed by HPLC analyses of nucleotide profiles of miaB mutants of E. coli. The insertion mutation was cloned and DNA sequences adjacent to the transposon were sequenced. These DNA sequences were 86% identical to the f474 gene at 14.97 min chromosome of E. coli. The f474 gene was then cloned by PCR from the wild-type chromosome of E. coli. The recombinant plasmid complemented the mutant phenotype of the miaB mutant of E. coli. These results support the hypothesis that the miaB gene of E. coli exists and is clonable. In summary, functions of the ms${2{\cdot}6}\atop1$A37 modification in E. coli cells are further delineated in this work in perspectives of adaptation to stressful environmental conditions and protein:tRNA interaction. (Abstract shortened by UMI.) ^