The systems-theoretic concept of controllability is elaborated for quantum-mechanical systems, sufficient conditions being sought under which the state vector ψ can be guided in time to a chosen point in the Hilbert space ℋ of the system. The Schrödinger equation for a quantum object influenced by adjustable external fields provides a state-evolution equation which is linear in ψ and linear in the external controls (thus a bilinear control system). For such systems the existence of a dense analytic domain 𝒟ω in the sense of Nelson, together with the assumption that the Lie algebra associated with the system dynamics gives rise to a tangent space of constant finite dimension, permits the adaptation of the geometric approach developed for finite-dimensional bilinear and nonlinear control systems. Conditions are derived for global controllability on the intersection of 𝒟ω with a suitably defined finite-dimensional submanifold of the unit sphere Sℋ in ℋ. Several soluble examples are presented to illuminate the general theoretical results.
STAT3 can be transcriptionally activated by phosphorylation of its tyrosine 705 or serine 727 residue. In mouse embryonic stem cells (mESCs), leukemia inhibitory factor (LIF) signaling maintains pluripotency by inducing JAK-mediated phosphorylation of STAT3 Y705 (pY705). However, the function of phosphorylated S727 (pS727) in mESCs remains unclear. In this study, we examined the roles of STAT3 pY705 and pS727 in regulating mESC identities, using a small molecule-based system to post-translationally modulate the quantity of transgenic STAT3 in STAT3−/− mESCs. We demonstrated that pY705 is absolutely required for STAT3-mediated mESC self-renewal, while pS727 is dispensable, serving only to promote proliferation and optimal pluripotency. S727 phosphorylation is regulated directly by fibroblast growth factor/Erk signaling and crucial in the transition of mESCs from pluripotency to neuronal commitment. Loss of S727 phosphorylation resulted in significantly reduced neuronal differentiation potential, which could be recovered by a S727 phosphorylation mimic. Moreover, loss of pS727 sufficed LIF to reprogram epiblast stem cells to naïve pluripotency, suggesting a dynamic equilibrium of STAT3 pY705 and pS727 in the control of mESC fate.
Embryonic stem cells (ESCs) can be maintained in culture indefinitely while retaining the capacity to generate any type of cell in the body, and therefore not only hold great promise for tissue repair and regeneration, but also provide a powerful tool for modeling human disease and understanding biological development. In order to fulfill the full potential of ESCs, it is critical to understand how ESC fate, whether to self-renew or to differentiate into specialized cells, is regulated. On the molecular level, ESC fate is controlled by the intracellular transcriptional regulatory networks that respond to various extrinsic signaling stimuli. In this review, we discuss and compare important signaling pathways in the self-renewal and differentiation of mouse, rat, and human ESCs with an emphasis on how these pathways integrate into ESC-specific transcription circuitries. This will be beneficial for understanding the common and conserved mechanisms that govern self-renewal, and for developing novel culture conditions that support ESC derivation and maintenance.
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