Networks, neutral

Urakawa H, Noble PA, El-Fantroussi S, Kelly JJ, Stahi DA (2002) Single base pair discrimination of terminal mismatches by using oligonucleotide microarrays and neutral network analyses. Appl Environ Microbiol 68 235-244... 

Cherqaoui, D. and Villemin, D. Use of a neutral network to determine the boiling point of alkanes, J. Chem. Soc., Faraday Trans., 90(1) 97-102, 1994. 

Andrews J, Lieberman S. 1994. Neutral-network approach to qualitative identification of fuels and oils from laser-induced fluorescence-spectra. Analytica Chimica Acta 285(l-2) 237-246. 

This equates the difference between the ionic contributions from the chemical potentials outside ( ) and inside the gel to the contributions of the two forces used to describe neutral networks. The contributions from the mixing and elastic portions of Eq. (17) may be described as discussed in Sect. 1.1 [13]. 

The general conclusion of the mentioned works was that the appearance of the jump on the dependences of network volume on the composition of the solvent or on temperature is reached only at some definite content of ionic groups in the network chains. For neutral networks with flexible chains, the collapse is usually not observed. Exceptions to this rule were reported for poly(isopropylacrylamide) (PIPAA) [16], poly(vinylcaprolactam) and poly-(2-vinylpyrrolidone) [17] gels. The specific feature of these systems is that the transition takes place in structured solvents water or concentrated aqueous solutions of aluminium sulfate. 

In the polyelectrolyte regime, due to the presence of low-molecular salt, the osmotic pressure of ions becomes less pronounced because the concentration of salt within the network turns out to be less than the concentration of salt in the outer solution n [27]. As the concentration ns grows, the amplitude of the jump of the dependence a(x) decreases and the jump shifts to the region of better solvents (Fig. 2, curve 2). At some critical value of n, the jump on the curve a(x) disappears, i.e. collapse of the network becomes smooth (Fig. 2, curve 3). Under the subsequent increase of n, the curve a(x) becomes closer and closer to the swelling curve of corresponding neutral network (Fig. 2, curves 4). 

As mentioned above, the discrete collapse of the gels is usually observed for charged networks. In Ref. [46], we showed that it is possible to obtain a jumpwise change of the dimensions for neutral networks by incorporation in a neutral gel of some charged linear macromolecules. In this case, the counter ions situated inside the network create there the same osmotic pressure as in the network, with some chemically connected charged groups. 

It is worthwhile mentioning here some other predictions which follow from the consideration of Sect. 2.3. For the gel, which has charges of one sign, the phase transition induced by elongating force should be sharper than for the neutral network. For a polyampholyte network near the isoelectric point, this transition is always continuous and even less pronounced than for the neutral gel. Finally, for the gel near the transition point, very small values of the applied force can induce a collapse of the gel or a jump-like swelling of the gel sample. 

A. Babajide, I.L. Hofacker, M.J. Sippl, and P.F. Stadler. Neutral networks in protein space - a computational study based on knowledge-based potentials of mean force. Folding Design, 2 261-269,1997. 

Reidys, C., Stadler, P.F., Schuster, P. (1996). Generic properties of combinatory maps. Neutral networks of RNA secondary structures. Bull. Math. Biol. 59,339-397. 

Na+/Ca2+ exchange, 260 Na+/K+ ATPase, 259-262 Neutral networks, 188-191 Nitrogenase, 212, 213 assay system, 212, 213 Nuclear transplantation, 268... 

Search on RNA secondary structure landscapes is distinctly different from search on the spin glass-like models. The difference is a result of the neutral networks that percolate the space. Note that, in practice, the sequences on neutral networks need not have exactly the same fitness, but fitnesses whose differences are below a threshold determined by the mutation rate and noise in the system. As with search on spin glass landscapes, this topic is quite extensive and is reviewed in several papers [39,67,69,113] as well as in Schuster s contribution to this collection, so I will only touch on a few key points. 

Rank r Size of the neutral network m Sequence of components Z... 

Sequences folding into the same structure form neutral networks in sequence space. A mathematical model based on random graph theory was designed [16] in order to allow for the derivation of analytical expressions. Neutral networks are represented by graphs in sequence space that show an interesting percolation phenomenon depending on the... 

Fig. 3. Neutral networks in sequence space. Depending on the fraction of nearest neighbors that are selectively neutral (X), the network is either partitioned into a largest component, the so-called giant component, and many small components (A X< Xcr) or it consists of a single component, usually spanning the whole sequence space (B X >Xcr). In case of RNA secondary structures, common structures form connected networks of type B.

Fig. 4. The role of neutral networks in evolutionary optimization through adaptive walks and random drift. Adaptive walks allow to choose the next step arbitrarily from all directions where fitness is (locally) nondecreasing. Populations can bridge over narrow valleys with widths of a few point mutations. In the absence of selective neutrality (upper part) they are, however, unable to span larger Hamming distances and thus will approach only the next major fitness peak. Populations on rugged landscapes with extended neutral networks evolve along the network by a combination of adaptive walks and random drift at constant fitness (lower part). In this manner, populations bridge over large valleys and may eventually reach the global maximum ofthe fitness landscape.

Sequences folding into the same structure form extended neutral networks that enable evolutionary dynamics to approach major peaks of fitness landscapes and eventually allow to reach the global optimum. 

Fig. 20. Movement through sequence space by continuous structural transitions. Each colored oval represents a structural neutral network. The transfer between neutral networks by continuous structural changes (solid arrows) is more likely than a sudden, discontinuous jump (dotted line).

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