SUMMARY In response to muscle injury, satellite cells activate the p38α/β MAPK pathway to exit quiescence, then proliferate, repair skeletal muscle, and self-renew, replenishing the quiescent satellite cell pool. Although satellite cells are capable of asymmetric division, the mechanisms regulating satellite cell self-renewal are not understood. We found that satellite cells, once activated, enter the cell cycle and a subset undergoes asymmetric division, renewing the satellite cell pool. Asymmetric localization of the Par complex activates p38α/β MAPK in only one daughter cell, inducing MyoD, which permits cell cycle entry and generates a proliferating myoblast. The absence of p38α/β MAPK signaling in the other daughter cell prevents MyoD induction, renewing the quiescent satellite cell. Thus, satellite cells employ a mechanism to generate distinct daughter cells, coupling the Par complex and p38α/β MAPK signaling to link the response to muscle injury with satellite cell self-renewal.

Somatic stem cells cycle slowly or remain quiescent until required for tissue repair and maintenance. Upon muscle injury, stem cells that lie between the muscle fiber and basal lamina (satellite cells) are activated, proliferate, and eventually differentiate to repair the damaged muscle. Satellite cells in healthy muscle are quiescent, do not express MyoD family transcription factors or cell cycle regulatory genes and are insulated from the surrounding environment. Here, we report that the p38α/β family of mitogen-activated protein kinases (MAPKs) reversibly regulates the quiescent state of the skeletal muscle satellite cell. Inhibition of p38α/β MAPKs (a) promotes exit from the cell cycle, (b) prevents differentiation, and (c) insulates the cell from most external stimuli allowing the satellite cell to maintain a quiescent state. Activation of satellite cells and p38α/β MAPKs occurs concomitantly, providing further support that these MAPKs function as a molecular switch for satellite cell activation.

We consider a class of dynamical systems on a compact Lie group G with a left-invariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, such systems can be regarded as generalized Chaplygin systems on the principle bundle G → Q = G/H, H being a Lie subgroup. In contrast to generic Chaplygin systems, the reductions of our LR systems onto the homogeneous space Q always possess an invariant measure.We study the case G = SO(n), when LR systems are multidimensional generalizations of the Veselova problem of a nonholonomic rigid body motion which admit a reduction to systems with an invariant measure on the (co)tangent bundle of Stiefel varieties V (k, n) as the corresponding homogeneous spaces.For k = 1 and a special choice of the left-invariant metric on SO(n), we prove that after a time substitution, the reduced system becomes an integrable Hamiltonian system describing a geodesic flow on the unit sphere S n−1 . This provides a first example of a nonholonomic system with more than two degrees of freedom for which the celebrated Chaplygin reducibility theorem is applicable for any dimension. In this case we also explicitly reconstruct the motion on the group SO(n).

Skeletal muscle satellite cells, which are found between the muscle fiber and the basal lamina, remain quiescent and undifferentiated unless stimulated to remodel skeletal muscle or repair injured skeletal muscle tissue. Quiescent satellite cells express c-met and fibroblast growth factor receptors (FGFR) 1 and 4, suggesting these receptors are involved in maintaining the undifferentiated quiescent state or involved in satellite cell activation. Although the signaling pathways involved are poorly understood, the mitogen activated protein kinase (MAPK) cascade has been implicated in the regulation of skeletal muscle growth and differentiation by FGFs. In this study, we investigated if activation of the Raf-MKK1/2-ERK1/2 signaling cascade plays a role in FGF-dependent repression of differentiation and proliferation of MM14 cells, a skeletal muscle satellite cell line. Inactivation ofthe Raf-MKK1/2-ERK1/2 pathway in myoblasts through the overexpression of dominant negative mutants of Raf-1 blocks ERK1/2 activity and prevents myoblast proliferation. Additionally, inhibition of MKK1/2 by treatment with pharmacological inhibitors also blocks FGF-mediated stimulation of ERK1/2 and blocks the G1 to S phase transition of myoblasts. Unexpectedly, we found that inactivation of the Raf-ERK pathway does not activate a muscle reporter, nor does inactivation of this pathway promote myogenic differentiation. We conclude that FGF-stimulated ERK1/2 signaling is required during the G1 phase of the cell cycle for commitment of myoblasts to DNA synthesis but is not required for mitosis once cells have entered the S-phase. Moreover, ERK1/2 signaling is not required either to repress differentiation, to promote skeletal muscle gene expression, or to promote myoblast fusion.

This paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two classical nonholonomic systems, the Suslov top and the Chaplygin sleigh. The preservation of the reduced energy by the discrete flow is observed and the discrete momentum conservation is discussed.

In this paper, we report the interaction of the CB[7] molecular container with crown ether styryl and (bis)styryl dyes 1-6. The interaction of monostyryl dyes (1 and 2) with CB[7] results in the formation of 1:1 complexes where the CB[7] molecule is located on the region of the guest encompassing the pyridinium ring, C=C double bond, and a portion of the aryl ring of benzocrown ethers 1 and 2. For (bis)styryl dyes (3-5), the formation of two types of complexes with composition dye.CB[7].dye and CB[7].dye.CB[7] was confirmed by a combination of optical and electrospray ionization mass spectroscopy (ESI-MS) methods. In the case of (bis)styryl dye (6), both 2:1 and 1:1 compositions 6.CB[7].6 and CB[7].6 were formed. Complex formation is accompanied by substantial changes in the optical characteristics of the dyes and formation of long-lived excimer species. We tested the stimuli responsiveness of this system in response to metal ions. We find that the metal ions prefer to bind to the electrostatically negative ureidyl C=O portals of the CB[7] rather than with the crown ether moiety of the styryl dyes.

An extension of the algebraic-geometric method for nonlinear integrable PDE's is shown to lead to new piecewise smooth weak solutions of a class of Ncomponent systems of nonlinear evolution equations. This class includes, among others, equations from the Dym and shallow water equation hierarchies. The main goal of the paper is to give explicit theta-functional expressions for piecewise smooth weak solutions of these nonlinear PDE's, which are associated to nonlinear subvarieties of hyperelliptic Jacobians.The main results of the present paper are twofold. First, we exhibit some of the special features of integrable PDE's that admit piecewise smooth weak solutions, which make them different from equations whose solutions are globally meromorphic, such as the KdV equation. Second, we blend the techniques of algebraic geometry and weak solutions of PDE's to gain further insight into, and explicit formulas for, piecewisesmooth finite-gap solutions.The basic technique used to achieve these aims is rather different from earlier papers dealing with peaked solutions. First, profiles of the finite-gap piecewise smooth solutions are linked to certain finite dimensional billiard dynamical systems and ellipsoidal billiards. Second, after reducing the solution of certain finite dimensional Hamiltonian systems on Riemann surfaces to the solution of a nonstandard Jacobi inversion problem, this is resolved by introducing new parametrizations.Amongst other natural consequences of the algebraic-geometric approach, we find finite dimensional integrable Hamiltonian dynamical systems describing the motion of peaks in the finite-gap as well as the limiting (soliton) cases, and solve them exactly. The dynamics of the peaks is also obtained by using Jacobi inversion problems. Finally, we relate our method to the shock wave approach for weak solutions of wave equations by determining jump conditions at the peak location.

Skeletal muscle satellite cells, which are found between the muscle fiber and the basal lamina, remain quiescent and undifferentiated unless stimulated to remodel skeletal muscle or repair injured skeletal muscle tissue. Quiescent satellite cells express c-met and fibroblast growth factor receptors (FGFR) 1 and 4, suggesting these receptors are involved in maintaining the undifferentiated quiescent state or involved in satellite cell activation. Although the signaling pathways involved are poorly understood, the mitogen activated protein kinase (MAPK) cascade has been implicated in the regulation of skeletal muscle growth and differentiation by FGFs. In this study, we investigated if activation of the Raf-MKK1/2-ERK1/2 signaling cascade plays a role in FGF-dependent repression of differentiation and proliferation of MM14 cells, a skeletal muscle satellite cell line. Inactivation ofthe Raf-MKK1/2-ERK1/2 pathway in myoblasts through the overexpression of dominant negative mutants of Raf-1 blocks ERK1/2 activity and prevents myoblast proliferation. Additionally, inhibition of MKK1/2 by treatment with pharmacological inhibitors also blocks FGF-mediated stimulation of ERK1/2 and blocks the G1 to S phase transition of myoblasts. Unexpectedly, we found that inactivation of the Raf-ERK pathway does not activate a muscle reporter, nor does inactivation of this pathway promote myogenic differentiation. We conclude that FGF-stimulated ERK1/2 signaling is required during the G1 phase of the cell cycle for commitment of myoblasts to DNA synthesis but is not required for mitosis once cells have entered the S-phase. Moreover, ERK1/2 signaling is not required either to repress differentiation, to promote skeletal muscle gene expression, or to promote myoblast fusion.