Holomorphic Analogs of Topological Gauge Theories

We introduce a new class of gauge field theories in any complex dimension, based on algebra-valued (p,q)-forms on complex n-manifolds. These theories are holomorphic analogs of the well-known Chern-Simons and BF topological theories defined on real manifolds. We introduce actions for different special holomorphic BF theories on complex, Kahler and Calabi-Yau manifolds and describe their gauge symmetries. Candidate observables, topological invariants and relations to integrable models are briefly discussed.Comment: 12 pages, LaTeX2e, shortened PLB versio

Mechanical stimulation induces formin-dependent assembly of a perinuclear actin rim

Proceedings of the National Academy of Sciences of the United States of America11220E2595-E260

A novel mechanism of actin filament processive capping by formin: solution of the rotation paradox

The FH2 domains of formin family proteins act as processive cappers of actin filaments. Previously suggested stair-stepping mechanisms of processive capping imply that a formin cap rotates persistently in one direction with respect to the filament. This challenges the formin-mediated mechanism of intracellular cable formation. We suggest a novel scenario of processive capping that is driven by developing and relaxing torsion elastic stresses. Based on the recently discovered crystal structure of an FH2–actin complex, we propose a second mode of processive capping—the screw mode. Within the screw mode, the formin dimer rotates with respect to the actin filament in the direction opposite to that generated by the stair-stepping mode so that a combination of the two modes prevents persistent torsion strain accumulation. We determine an optimal regime of processive capping, whose essence is a periodic switch between the stair-stepping and screw modes. In this regime, elastic energy does not exceed feasible values, and supercoiling of actin filaments is prevented

Focal Contacts as Mechanosensors: Externally Applied Local Mechanical Force Induces Growth of Focal Contacts by an Mdia1-Dependent and Rock-Independent Mechanism

The transition of cell–matrix adhesions from the initial punctate focal complexes into the mature elongated form, known as focal contacts, requires GTPase Rho activity. In particular, activation of myosin II–driven contractility by a Rho target known as Rho-associated kinase (ROCK) was shown to be essential for focal contact formation. To dissect the mechanism of Rho-dependent induction of focal contacts and to elucidate the role of cell contractility, we applied mechanical force to vinculin-containing dot-like adhesions at the cell edge using a micropipette. Local centripetal pulling led to local assembly and elongation of these structures and to their development into streak-like focal contacts, as revealed by the dynamics of green fluorescent protein–tagged vinculin or paxillin and interference reflection microscopy. Inhibition of Rho activity by C3 transferase suppressed this force-induced focal contact formation. However, constitutively active mutants of another Rho target, the formin homology protein mDia1 (Watanabe, N., T. Kato, A. Fujita, T. Ishizaki, and S. Narumiya. 1999. Nat. Cell Biol. 1:136–143), were sufficient to restore force-induced focal contact formation in C3 transferase-treated cells. Force-induced formation of the focal contacts still occurred in cells subjected to myosin II and ROCK inhibition. Thus, as long as mDia1 is active, external tension force bypasses the requirement for ROCK-mediated myosin II contractility in the induction of focal contacts. Our experiments show that integrin-containing focal complexes behave as individual mechanosensors exhibiting directional assembly in response to local force

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

Comparative Dynamics of Retrograde Actin Flow and Focal Adhesions: Formation of Nascent Adhesions Triggers Transition from Fast to Slow Flow

Dynamic actin network at the leading edge of the cell is linked to the extracellular matrix through focal adhesions (FAs), and at the same time it undergoes retrograde flow with different dynamics in two distinct zones: the lamellipodium (peripheral zone of fast flow), and the lamellum (zone of slow flow located between the lamellipodium and the cell body). Cell migration involves expansion of both the lamellipodium and the lamellum, as well as formation of new FAs, but it is largely unknown how the position of the boundary between the two flow zones is defined, and how FAs and actin flow mutually influence each other. We investigated dynamic relationship between focal adhesions and the boundary between the two flow zones in spreading cells. Nascent FAs first appeared in the lamellipodium. Within seconds after the formation of new FAs, the rate of actin flow decreased locally, and the lamellipodium/lamellum boundary advanced towards the new FAs. Blocking fast actin flow with cytochalasin D resulted in rapid dissolution of nascent FAs. In the absence of FAs (spreading on poly-L-lysine-coated surfaces) retrograde flow was uniform and the velocity transition was not observed. We conclude that formation of FAs depends on actin dynamics, and in its turn, affects the dynamics of actin flow by triggering transition from fast to slow flow. Extension of the cell edge thus proceeds through a cycle of lamellipodium protrusion, formation of new FAs, advance of the lamellum, and protrusion of the lamellipodium from the new base

Reinforcement versus Fluidization in Cytoskeletal Mechanoresponsiveness

Every adherent eukaryotic cell exerts appreciable traction forces upon its substrate. Moreover, every resident cell within the heart, great vessels, bladder, gut or lung routinely experiences large periodic stretches. As an acute response to such stretches the cytoskeleton can stiffen, increase traction forces and reinforce, as reported by some, or can soften and fluidize, as reported more recently by our laboratory, but in any given circumstance it remains unknown which response might prevail or why. Using a novel nanotechnology, we show here that in loading conditions expected in most physiological circumstances the localized reinforcement response fails to scale up to the level of homogeneous cell stretch; fluidization trumps reinforcement. Whereas the reinforcement response is known to be mediated by upstream mechanosensing and downstream signaling, results presented here show the fluidization response to be altogether novel: it is a direct physical effect of mechanical force acting upon a structural lattice that is soft and fragile. Cytoskeletal softness and fragility, we argue, is consistent with early evolutionary adaptations of the eukaryotic cell to material properties of a soft inert microenvironment