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.

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.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

IDENTIFICATION AND ANALYSIS OF A NOVEL ROLE FOR THE TOUSLED-LIKE KINASE IN REGULATING MITOTIC SPINDLE DYNAMICS

Deregulation of kinase activity is one example of how cells become cancerous by evading evolutionary constraints. The Tousled kinase (Tsl) was initially identified in Arabidopsis thaliana as a developmentally important kinase. There are two mammalian orthologues of Tsl and one orthologue in C. elegans, TLK-1, which is essential for embryonic viability and germ cell development. Depletion of TLK-1 leads to embryonic arrest large, distended nuclei, and ultimately embryonic lethality. Prior to terminal arrest, TLK-1-depleted embryos undergo aberrant mitoses characterized by poor metaphase chromosome alignment, delayed mitotic progression, lagging chromosomes, and supernumerary centrosomes. I discovered an unanticipated requirement for TLK-1 in mitotic spindle assembly and positioning. Normally, in the newly-fertilized zygote (P0) the maternal pronucleus migrates toward the paternal pronucleus at the posterior end of the embryo. After pronuclear meeting, the pronuclear-centrosome complex rotates 90° during centration to align on the anteroposterior axis followed by nuclear envelope breakdown (NEBD). However, in TLK-1-depleted P0 embryos, the centrosome-pronuclear complex rotation is significantly delayed with respect to NEBD and chromosome congression, Additionally, centrosome positions over time in tlk-1(RNAi) early embryos revealed a defect in posterior centrosome positioning during spindle-pronuclear centration, and 4D analysis of centrosome positions and movement in newly fertilized embryos showed aberrant centrosome dynamics in TLK-1-depleted embryos. Several mechanisms contribute to spindle rotation, one of which is the anchoring of astral microtubules to the cell cortex. Attachment of these microtubules to the cortices is thought to confer the necessary stability and forces in order to rotate the centrosome-pronuclear complex in a timely fashion. Analysis of a microtubule end-binding protein revealed that TLK-1-depleted embryos exhibit a more stochastic distribution of microtubule growth toward the cell cortices, and the types of microtubule attachments appear to differ from wild-type embryos. Additionally, fewer astral microtubules are in the vicinity of the cell cortex, thus suggesting that the delayed spindle rotation could be in part due to a lack of appropriate microtubule attachments to the cell cortex. Together with recently published biochemical data revealing the Tousled-like kinases associate with components of the dynein microtubule motor complex in humans, these data suggest that Tousled-like kinases play an important role in mitotic spindle assembly and positioning.