Graded Contractions Research Articles

Cooling-induced gastrointestinal smooth muscle contractions in the rat.

The aim of this study was to assess the effect of cooling on smooth muscle contraction in various parts of the gastrointestinal tract (esophagus, stomach, duodenum, jejunum and colon) and to investigate the basic mechanism underlying cooling-induced (CIC) tonic and rhythmic contractions. Recordings of isometric tension from smooth muscle strips of different parts of the rat gastrointestinal tract were performed using organ-bath techniques, and stepwise cooling was applied. Cooling was tested before and after the addition of various standard agents interfering with known neurogenic (autonomic blockers, tetrodotoxin, capsaicin) and myogenic mechanisms of contraction (calcium channel blockers, Sarcoplasmatic and Ca2+-ATPase pump inhibitors). Step-wise cooling (37 degrees C to 5 degrees C) of all gastrointestinal smooth muscle preparations induced reproducible graded tonic contractions, inversely proportional to temperature. CIC was most pronounced in the jejunum. Cooling abolished rhythmic smooth muscle activity. CIC was not dependent on a neural mechanism nor the release of neurotransmitters, but linked to translocation of calcium. It was reduced by incubation in Ca2+-free solution. Blockage of the Ca2+-ATPase pump, which inhibits the extrusion of calcium, plays a significant role in the process and enhances CIC. Cooling of gastrointestinal smooth muscle preparations induces graded myogenic contractions inversely proportional to the temperature. The mechanism is not dependent on local nervous control but related to a temperature-sensitive process of calcium translocation.

Modules of graded contracted Virasoro algebras

We have described graded contractions of the Virasoro algebra. The highest weight representations of the Virasoro algebra have been constructed. The reducibility of representations is analised. In contrast to standard representations the contracted ones are reducible except some special cases. Moreover we have found an exotic module with null-plane on the fifth level.

On fine gradings and their symmetries

In this paper fine gradings ofgl(n, C) associated with the Pauli matrices inn dimensions are studied with the subsequent graded contractions ofsl(n, C) in view. It is shown that, ifn≥3 is a prime, the discrete symmetries of the gradings involve the specialn-dimensional representations ofSL(2,F n), whereF n is the finite field of ordern. These symmetries may be used to simplify the system of contraction equations.

Graded contractions of Lie algebras and central extensions*

We use the concept of grading of Lie algebras to investigate the appearance of central charges during the contraction process. As for the usual graded contractions, one finds simultaneously the central extensions of classes of algebras, rather than specific Lie algebras. To illustrate the method, we consider in detail two physical applications: the kinematical algebras of spacetime and the u(n)-bosons limits of some Lie algebras.

Muscle recruitment through electrical stimulation of the lumbo-sacral spinal cord.

The goal of this study was to determine the feasibility of producing graded muscle contraction in individual muscles or muscle groups by electrically stimulating motor neurons in the lumbo-sacral spinal cord. Recruitment curves were obtained for quadriceps, tibialis anterior and triceps surae/plantaris by stimulating their activation pools in the ventral horn of the feline spinal cord. Mean twitch times-to-peak for quadriceps, tibialis anterior and triceps surae/plantaris were 33.0, 41.0, and 36.0 ms, respectively. Twitch duration as a function of stimulus strength demonstrated a mixed motor unit recruitment order, distinctively different from the inverse recruitment order exhibited by conventional methods of electrical stimulation of peripheral nerve. The recruitment curve slopes (expressed as a percentage of maximum force per nanocurrent of delivered charge) were shallow: 7.9 for quadriceps, 2.6 for tibialis anterior and 8.5 for triceps surae/plantaris. These results show that graded control of force in individual muscles or muscle groups can be obtained through spinal cord stimulation, and suggest that spinal cord stimulation could be used for functional neuromuscular stimulation applications.

Cooling-induced bladder contraction: studies on isolated detrusor muscle preparations in the rat

Objectives. Detrusor muscle contraction and uninhibited micturition after intravesical instillation of ice water is interpreted as a sign of upper motor neuron lesions. The basic mechanism of cooling-induced contraction (CIC) at the level of smooth muscle, however, has not been satisfactorily explained. We therefore designed model experiments with cooling of rat detrusor muscle. Methods. We recorded isometric tension from strips of rat urinary detrusor muscle in organ baths during stepwise cooling. CIC was tested before and after addition of various standard agents interfering with known neurogenic (autonomic blockers, tetrodotoxin, capsaicin) and myogenic mechanisms of contraction (calcium channel blockers). Results. Stepwise cooling (37° to 5°C) of detrusor muscle induced reproducible graded contractions, inversely proportional to temperature. CIC was not dependent on a neural mechanism (not blocked by tetrodotoxin or capsaicin) or the release of neurotransmitters but was linked to translocation of calcium. It was reduced by calcium channel blockers and Ca 2+-free solution. Blockage of the Ca 2+-adenosine triphosphatase pump, which inhibits the extrusion of calcium, also plays a significant role in the process and enhances CIC. Conclusions. Cooling of detrusor muscle preparations induces a graded myogenic contraction inversely proportional to the temperature. The mechanism is not dependent on local nervous control but is related to calcium translocation.

Graded contractions of the Lie algebrae(2, 1)

The graded contractions of pseudo-Euclidean Lie algebra are studied. The non-equivalent gradings of of type and a are extended to the entire Lie algebra , using the action of on the Abelian ideal (the translations.). The graded contractions embed into a large family of six-dimensional Lie algebras. The family includes solvable, nilpotent and nonsolvable Lie algebras, both decomposable and indecomposable ones. The distinction between graded and Inonu-Wigner contractions is analysed. The physically most interesting Lie algebras obtained by the contractions are the inhomogeneous Galilei and pseudo-Galilei.

Systems to enhance the ability to Farm to Specification, a farmer's perspective

What do we mean when we talk about Farming to Specification? As a farmer, I take that to mean supplying a product that has been farmed to required Quality Assurance Standards and presented to a processor on time, in full and to market specification. Processing and marketing companies have started to demand tighter guidelines for product supplied and there is no doubt in my mind that the tightening trend will continue. We already have a number of companies offering fixed price and grade contracts, with severe penalties for non-supply, and I am sure that these contracts will become commonplace within the Sheep, Beef and Deer industries. Our major customers in overseas markets are demanding guaranteed and consistent supply year round. The main threat that we face in our ability to supply product to specification is the climate and the influence it has on pasture production and animal performance. It is imperative that we have systems in place to take full advantage of opportunities when the climate is favourable, but also when the climate is challenging. My paper today will focus on the systems we have developed that enhance our ability to farm to market specification for sheep beef and deer.

Successive Refinements of Gradings and Graded Contractions of sl(3,C)

All toroidal gradings of sl (3,C) are presented and used to obtain graded contractions of this Lie algebra. There exist 34 classes of Lie algebra obtained by the contractions. Most of them are obtained using the coarsest (an hence simplest) gradings (Z2, Z3 and Z4 ones).

Grading refinements in the contractions of Lie algebras and their invariants

All mutually inequivalent toroidal gradings of the Lie algebra are constructed. Each of them provides several different graded contractions to other eight-dimensional Lie algebras. These can be either continuous, or discrete. The continuous ones are related to generalized Wigner - Inonu contractions. The behaviour of Casimir operators under the graded contractions is studied and the Casimir and generalized Casimir operators of the contracted Lie algebras are presented.

All-or-none contraction and sodium channels in a subset of circular muscle fibers of squid mantle.

Motor function in squid (Loligo) mantle reflects the highly coordinated activity of two motor pathways associated with giant and non-giant motor axons that respectively produce all-or-none and graded contractions in mantle muscle. Whereas both types of axons innervate circular mantle muscle fibers, precise nerve-muscle relationships remain unclear. Are squid like most invertebrates, in which single muscle fibers receive dual innervation from giant and non-giant motor axons, or is squid mantle configured more like vertebrates, in which parallel motor axon systems innervate distinct fast and slow muscle fibers? In this report, we describe giant and nongiant motor pathways that appear to control different pools of circular muscle fibers in squid. A subset of circular muscle fibers possesses large Na currents, and these fibers are proposed to employ Na-dependent action potentials to produce fast, all-or-none muscle twitches associated with giant axon stimulation.

The general solution of the real graded contractions of

The general solution of the graded contraction equations for a grading of the real compact simple Lie algebra so(N+1) is presented in an explicit way. It turns out to depend on independent real parameters. The structure of the general graded contractions is displayed for the low-dimensional cases, and kinematical algebras are shown to appear straightforwardly. The geometrical (or physical) meaning of the contraction parameters as curvatures is also analysed; in particular, for kinematical algebras these curvatures are directly linked to geometrical properties of possible homogeneous spacetimes.

Contractions of Lie algebras: Generalized Inönü–Wigner contractions versus graded contractions

Recently, a new notion of contraction has been introduced, the purely algebraically defined graded contractions that fall into two disjoint classes: continuous and discrete. Our main result is that all continuous graded contractions can be realized by generalized Inönü–Wigner contractions. Furthermore, we give a complete characterization of the discrete graded contractions via certain higher-order identities inherent to the grading group.

Cayley-Klein algebras as graded contractions of so(N+1)

We study $\Bbb Z_2^{\otimes N}$ graded contractions of the real compact simple Lie algebra $so(N+1)$, and we identify within them the Cayley-Klein algebras as a naturally distinguished subset.

Calcium Dependence of Contractile Activation of Isolated Sheep Urethra II: Responses to Exogenous Noradrenaline

Isolated smooth muscle of sheep urethra responded to exogenous noradrenaline (NA) with a concentration-dependent contraction. After exposing the preparations for 30 min. to calcium-free medium, NA in a submaximal concentration was still able to produce a contractile response amounting to 36% of control value in calcium-containing solution. Readmission of calcium (administered cumulatively) restored the response in a concentration-related fashion to 85% (at 5 mM calcium) of control level. Nifedipine and verapamil failed to inhibit these graded calcium contractions in the presence of NA. Verapamil and diltiazem also failed to significantly prevent contraction induced by NA in a submaximum concentration, but nifedipine showed a concentration-dependent inhibitory effect, with a potency 1000 times lower than that observed on K+ (124 mM) induced contractions. In calcium-free medium, repeated applications of NA at 30 min. intervals, induced a progressive reduction in contractile amplitude. Nifedipine or verapamil did not affect the time course for recovery of NA-induced contraction when the preparations were returned to calcium containing medium, but the recovery was blocked almost completely by lanthanum. Furthermore, lanthanum abolished the remaining NA contraction in calcium-free medium. The results suggest that NA-induced contraction in isolated sheep urethra is dependent on both influx of extracellular calcium and on release of intracellular calcium. Calcium influx for contractile activation and refilling of intracellular stores seem to occur through membrane channels that can only partly be blocked with calcium antagonists.

Discrete and continuous graded contractions of representations of Lie algebras

Simultaneous grading of Lie algebras and their representation spaces is used to develop a new theory of grading preserving contractions of representations of all Lie algebras admitting the chosen grading. The theory is completely different from the traditional ways of contracting representations. The graded contractions fall naturally into two classes: discrete and continuous ones related respectively to 2-cocycles and coboundaries of the grading group.

Matching neural and muscle oscillators: control by FMRFamide-like peptides

Stomatogastric nervous systems of the shrimp, Palaemon serratus, were stained with antisera raised against the peptide FMRFamide. FMRFamide-like immunoreactivity was found in fibers in the input nerve to the stomatogastric ganglion (STG), in several STG somata, in dense neuropil in the STG, in the motor nerves that innervate the dilator muscles of the pyloric region, but not in the pyloric dilator (PD) motor neurons. FMRFamide and several FMRFamide-like peptides elicited sequences of rhythmic depolarizations and contractions of the pyloric dilator muscle. As peptide concentrations were increased, a discrete threshold for contraction was found, above which contractions were initiated with a decreasing latency in an all-or-none fashion. Muscles stopped rhythmically contracting after many seconds to several minutes of activity; the duration of spontaneous oscillatory activity in peptide was proportional to the concentration of applied peptide. In the absence of peptide, each motor neuron discharge evoked small graded muscle contractions. During peptide-induced oscillations, motor neuron activity did not always entrain muscle oscillations. After spontaneous oscillations had stopped, when the motor neurons were stimulated in the presence of the peptide, each motor neuron burst evoked large amplitude contractions as a result of the peptide-induced regenerative properties of the muscle membrane.

Tentacle autotomy in the hydromedusa Aglantha digitale (Cnidaria): an ultrastructural and neurophysiological analysis

Tentacles of the hydromedusa Aglantha digitate readily detach (autotomize) at a predictable site (autotomy plane) when a tentacle is pinched and tugged. The response is reversibly inhibited in seawater containing excess Mg 2+ . Behavioural, electrophysiological and ultrastructural analyses indicate that passive and active processes are involved in tentacle autotomy. Inherent structural weakness at the tentacle autotomy plane is suggested by thinning of mesoglea and reduction of muscle tails at this site. The autotomy plane is also characterized by a ring of distinctive ectodermal cells with vacuoles concentrated along the basal cell membrane bordering the mesoglea. These vacuolated autotomy plane (VAP) cells are extensively innervated and, except for a few slender muscle tails, they interrupt the sheath of myoepithelium encasing each tentacle. Tentacles fixed after an autotomizing stimulus but before tentacle breakage show loss of basal vacuoles in VAP cells and holes in the underlying mesoglea. We suggest that the active mechanisms for tentacle autotomy include strong contraction of muscle tails on either side of the autotomy plane and activation of VAP cells, which somehow lower the tensile strength of autotomy plane mesoglea. Autotomizing stimuli do not appear to evoke a special conduction system within the tentacle. Highfrequency nerve-impulse activity in the tentacle conduction system that otherwise directs graded tentacle contractions is initiated by autotomizing stimuli and precedes tentacle disjunction. Tentacle autotomy in Aglantha , a delicate holopelagic hydromedusa that inhabits densely populated pelagic zones, may allow escape when the tentacles inadvertently entangle and overly large and potentially damaging zooplankters.

Discrete and continuous graded contractions of Lie algebras and superalgebras

Grading preserving contractions of Lie algebras and superalgebras of any type over the complex number field are defined and studied. Such contractions fall naturally into two classes: the Wigner-Inonu-like continuous contractions and new discrete contractions. A general method is described for any Abelian grading semigroup and any Lie algebra or superalgebra admitting such a grading. All contractions preserving z2-, z3-, and z2*z2-gradings are found. Examples of these gradings and contractions for the simple Lie algebra A2, affine Kac-Moody algebra A(1) and the simple superalgebra osp(2,1) are shown.

Several graded contractions on Hilbert space

In this paper we define the concept of amplification for several commuting contractions on Hilbert space. The question of symbolic calculus for such contractions is addressed and reduced to a special case in which the contractions are independent unilateral shifts at least on the algebraic level. Using amplifications, this question is further reduced to the case in which the underlying “geometry” of the Hilbert space is “maximal”. In the case of one or two contractions, these maximal geometries correspond to the case in which the contractions are isometries. For three or more contractions, the structure of maximal geometries remains a mystery. Based on this approach, we prove some new results on symbolic calculus—generalizations of the inequalities of von Neumann and Ando. The most interesting result is for homogenous polynomials whose spectrum is “centrally located”. Some of these ideas apply with routine modifications to the case where the contractions do not necessarily commute. We also discuss cases where some commutations are allowed, but not others.