Loop entropy model

There is an alternative way of deriving (2.3d) which we present here because it is a more natural way to analyze loop entropy models and the hairpinning effect. Let us consider a DNA molecule composed of a respected sequence of identical base pairs and in a bonding state such that there is a set of runs of /j successive bound base pairs, followed by m, successive broken bond base pairs, bound, broken, bound... 

To proceed further we must postulate some form for the weights g(l) and f(m). At this point we accept the MI form for these later, when considering the loop entropy models, other forms will be analyzed. In the nearest neighbor MI case we set... 

When we treat the loop entropy model and the hairpin branches we use the preceding ideas but give an alternative form to the weight function f m) for unbonded regions. 

Basically, there are two different models that have been applied to the helix-coil transition of DNA, These models differ mainly in the treatment of a loop of broken bonds sandwiched between two helical segments. The modified Ising (MI) model considers the unwinding of the interior of a DNA molecule to take place in the same manner as the free ends. The loop entropy (LE) model accounts for a differpuce between the entropy of unbonded strands sandwiched between two helical sections and the entropy of unbonded strands at the end of the molecule. 

The modified Ising (MI) model has been applied to the DNA transition by several authors.Although the underlying model employed by these authors has been the same, the methods and approximations made have been different. The notation used in these calculations has also varied, and we will endeavor to show their connection where appropriate. Although the MI model omits the loop entropy factor, its simplicity allows an easy comparison with experiment and gives a basis for further improvements. We first obtain the melting curves of periodic DNAs and then present results for DNAs with a random distribution of A-T and G-C base pairs. 

The model just described accounts for the basic interactions needed in a cooperative transition but fails to include several factors. Correlations between base pairs more remote than nearest ones was not explicitly considered. Since we would expect the long-range correlations to damp out rapidly, this is probably not too important. Another factor that has been omitted in the previous model is the loop entropy. This is the configurational entropy which remains in unbonded strands after connecting bonds are broken. This entropy will depend on the size of the unbonded strands or loop and the flexibility of the DNA strands. 

For both the one- and two-component DNAs described by the LE model, the form of is slightly changed from that used in the MI model for similar DNAs [(2.21) and (2.26)]. For the MI model = 0 at r = for the unbranched periodic DNAs. This is not exactly true in the LE model due to the inclusion of the loop entropy factor. Instead, we have... 

A proper theoretical examination of poly d(A-T)-poly [Pg.178]

The Poland Scheraga model is introduced by assigning the so called loop entropy S ) which is taken with the property... 

One problem with the network equations is that they can, on occasion, give rise to negative bond valences which have no physical significance (expect to indicate that, from a chemical point of view, the bond should not exist). Rutherford (1998) has explored the resonance bond model as an alternative to the use of the loop equation (Section 14.4) while Rao and Brown (1998) have suggested using the method of maximum entropy (Section 11.2.2.1). 

As described above for elastin and resilin, the ability of elastomeric proteins to exhibit elasticity relies on the molecular movement, stmctural folding, and conformational freedom of individual components so that they can instantaneously respond to the applied force within a cross-linked network to distribute the stress throughout the system. Stretching initially will interrupt interactions between the loops such as hydrophobic interactions, hydrogen bonding, and electrostatic interactions, while at higher extensions a decrease in conformational entropy will be prevalent. To date, different models are proposed to explain the mechanisms of elasticity for resilin, based on the knowledge from elasticity models that have been proposed for elastin. 

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