Non-Abelian Stokes Theorem and Quark Confinement in SU(3) Yang-Mills Gauge Theory

We derive a new version of SU(3) non-Abelian Stokes theorem by making use of the coherent state representation on the coset space $SU(3)/(U(1)\times U(1))=F_2$, the flag space. Then we outline a derivation of the area law of the Wilson loop in SU(3) Yang-Mills theory in the maximal Abelian gauge (The detailed exposition will be given in a forthcoming article). This derivation is performed by combining the non-Abelian Stokes theorem with the reformulation of the Yang-Mills theory as a perturbative deformation of a topological field theory recently proposed by one of the authors. Within this framework, we show that the fundamental quark is confined even if $G=SU(3)$ is broken by partial gauge fixing into $H=U(2)$ just as $G$ is broken to $H=U(1) \times U(1)$. An origin of the area law is related to the geometric phase of the Wilczek-Zee holonomy for U(2). Abelian dominance is an immediate byproduct of these results and magnetic monopole plays the dominant role in this derivation.Comment: 14 pages, Latex, no figures, version accepted for publication in Mod. Phys. Lett. A (some comments are added in the final parts

Asymmetric requirement of Dpp/BMP morphogen dispersal in the Drosophila wing disc

How morphogen gradients control patterning and growth in developing tissues remains largely unknown due to lack of tools manipulating morphogen gradients. Here, we generate two membrane-tethered protein binders that manipulate different aspects of Decapentaplegic (Dpp), a morphogen required for overall patterning and growth of the Drosophila wing. One is "HA trap" based on a single-chain variable fragment (scFv) against the HA tag that traps HA-Dpp to mainly block its dispersal, the other is "Dpp trap" based on a Designed Ankyrin Repeat Protein (DARPin) against Dpp that traps Dpp to block both its dispersal and signaling. Using these tools, we found that, while posterior patterning and growth require Dpp dispersal, anterior patterning and growth largely proceed without Dpp dispersal. We show that dpp transcriptional refinement from an initially uniform to a localized expression and persistent signaling in transient dpp source cells render the anterior compartment robust against the absence of Dpp dispersal. Furthermore, despite a critical requirement of dpp for the overall wing growth, neither Dpp dispersal nor direct signaling is critical for lateral wing growth after wing pouch specification. These results challenge the long-standing dogma that Dpp dispersal is strictly required to control and coordinate overall wing patterning and growth

Asymmetric requirement of Dpp/BMP morphogen dispersal in the Drosophila wing disc

How morphogen gradients control patterning and growth in developing tissues remains largely unknown due to lack of tools manipulating morphogen gradients. Here, we generate two membrane-tethered protein binders that manipulate different aspects of Decapentaplegic (Dpp), a morphogen required for overall patterning and growth of the Drosophila wing. One is "HA trap" based on a single-chain variable fragment (scFv) against the HA tag that traps HA-Dpp to mainly block its dispersal, the other is "Dpp trap" based on a Designed Ankyrin Repeat Protein (DARPin) against Dpp that traps Dpp to block both its dispersal and signaling. Using these tools, we found that, while posterior patterning and growth require Dpp dispersal, anterior patterning and growth largely proceed without Dpp dispersal. We show that dpp transcriptional refinement from an initially uniform to a localized expression and persistent signaling in transient dpp source cells render the anterior compartment robust against the absence of Dpp dispersal. Furthermore, despite a critical requirement of dpp for the overall wing growth, neither Dpp dispersal nor direct signaling is critical for lateral wing growth after wing pouch specification. These results challenge the long-standing dogma that Dpp dispersal is strictly required to control and coordinate overall wing patterning and growth

Asymmetric requirement of Dpp/BMP morphogen dispersal in the Drosophila wing disc

Morphogen gradients provide positional information and control growth in developing tissues, but the 24 underlying mechanisms remain largely unknown due to lack of tools manipulating morphogen 25 gradients. Here, we generate two synthetic protein binder tools manipulating different parameters of 26 Decapentaplegic (Dpp), a morphogen thought to control Drosophila wing disc patterning and growth 27 by dispersal; while HA trap blocks Dpp dispersal, Dpp trap blocks Dpp dispersal and signaling in the 28 source cells. Using these tools, we found that while posterior patterning and growth require Dpp 29 dispersal, anterior patterning and growth largely proceed without Dpp dispersal. We show that dpp 30 transcriptional refinement from an initially uniform to a localized expression and persistent signaling 31 in transient dpp source cells render the anterior compartment robust to blocking Dpp dispersal. 32 Furthermore, neither Dpp dispersal nor signaling is critical for lateral wing growth. These results 33 challenge Dpp dispersal-centric mechanisms, and demonstrate the utility of customized protein binder 34 tools to dissect protein functions