Limit cycle Link” system

Selected entries from Methods in Enzymology [vol, page(s)] Analysis of GTP-binding/GTPase cycle of G protein, 237, 411-412 applications, 240, 216-217, 247 246, 301-302 [diffusion rates, 246, 303 distance of closest approach, 246, 303 DNA (Holliday junctions, 246, 325-326 hybridization, 246, 324 structure, 246, 322-324) dye development, 246, 303, 328 reaction kinetics, 246, 18, 302-303, 322] computer programs for testing, 240, 243-247 conformational distribution determination, 240, 247-253 decay evaluation [donor fluorescence decay, 240, 230-234, 249-250, 252 exponential approximation of exact theoretical decay, 240, 222-229 linked systems, 240, 234-237, 249-253 randomly distributed fluorophores, 240, 237-243] diffusion coefficient determination, 240, 248, 250-251 diffusion-enhanced FRET, 246, 326-328 distance measurement [accuracy, 246, 330 effect of dye orientation, 246, 305, 312-313 limitations, 246,... 

It was pointed out earlier that oscillations in NDR oscillators are linked to three features of the electrochemical system (1) an N-shaped steady-state polarization curve (2) a resistance in series with the working electrode, which must not be too large and (3) a slow recovery of the electroactive species, in most cases due to slow mass transport. Hence, for every system that was discussed in the context of the possible origin of N-shaped characteristics, conditions can be estabhshed under which stable limit cycles exist, and for most of the systems mentioned, oscillations were in fact observed. This unifying approach was first put forth by Koper and Sluyters, and numerous experimental examples of electrochemical oscillations that can be deduced according to this mechanism are discussed in Ref. 60. 

All results established in chapter 2 for the analysis of eqns (2.7) in the phase plane therefore also apply to the two-variable system (5.4b,c). In particular, the two nullclines of the system remain defined by eqns (2.21). When parameter A exceeds a critical value, the product nullcline y= 4> takes the form of a sigmoid possessing a region in which the slope (da/dy) is negative in the phase plane (a, y). When the substrate nullcline v = a intersects the product nullcline in that region, in such a manner that condition (2.26) is satisfied, the steady state, which lies at the intersection of the two nullclines, is unstable and the system evolves towards a limit cycle corresponding to sustained oscillations (fig. 2.13). Such behaviour translates here into oscillations of ATP and extracellular cAMP, to which are associated oscillations in intracellular cAMP because of relation (5.4a), which links to the slower variables a and y. 

In the case where the physical system can be adequately modeled by a dynamical system on the plane, precise mathematical meaning can be given to this feature of physical robustness , and this was done by Andronov. First of all, he applied the Poincare theory of limit cycles and the Lyapunov theory of stability for studying modeling equations that allowed him and Vitt to explain many real phenomena in radio-engineering. Then, he linked the... 

In summary, current evidence [39-41] is thus consistent with the view that the ferredoxin/thioredoxin system functions in photosynthetically diverse types of plants as a master switch to restrict the activity of degradatory enzymes and activate biosynthetic enzymes in the light. It is significant that enzymes controlled by the ferredoxin/thioredoxin system (FBPase, SBPase, NADP-G3PDH, and PRK) function in the regenerative phase of the reductive pentose phosphate cycle that is needed to sustain its continued operation - i.e, to regenerate the carbon dioxide acceptor, Rbu-1,5-P2, from newly formed 3-PGA. It seems likely that one of these thioredoxin-linked enzymes limits the regeneration of Rbu-1,5-P2. 

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