Isochore strict

Figure 11.5 compares the fluid entropy vectors, whose lengths range from about 0.25 (ideal gas) to about 0.75 (ether). As expected, the entropy vectors exhibit an approximate inverted or complementary (conjugate) relationship to the corresponding T vectors of Fig. 11.3. The length of each S vector reflects resistance to attempted temperature change (under isobaric conditions), i.e., the capacity to absorb heat with little temperature response. The lack of strict inversion order with respect to the T lengths of Table 11.3 reflects subtle heat-capacity variations between isochoric and isobaric conditions, as quantified in the heat-capacity or compressibility ratio...

This result appears to be counterintuitive, especially since we normally allow the energy to depend on mole numbers, as specified by the relation E = E S, V, N( ). However, this problem is apparent rather than real from the viewpoint of chemistry the fundamental species in any chemical reaction are the participating atoms whose numbers are strictly conserved—witness the process of balancing any chemical equation. Thus, while the arrangement or configuration of the atoms changes in a chemical process their numbers are not altered in this process. Under conditions of strict isolation the system behaves as a black box no indication of the internal processes is communicated to the outside. One should not attempt to describe processes to which one has no direct access. However, under conditions illustrated in Remark 1.21.2, even an isochoric reaction carried out very slowly in strict isolation, produces an entropy change dS = dO = 1 Hi dNi > 0. See also Eq. (2.9.3) which proves Eq. (1.21.3) under equilibrium conditions. 

This is the van t Hoff isochore (or isobar) equation. We shall use this equation often, although, at first sight, it seems not to be very helpful. Strictly speaking, there are four variables, K, AH°, T and AS0, although only K varies widely with temperature. However, it is worth while to look more closely at Alt1 and AS0, and their variation with temperature. 

The second paper (Lander et al., 2001 also referred to as International Human Genome Sequencing Consortium, 2001) studied the draft genome sequence to see whether strict isochores could be identified and failed to find any. They concluded that their results rule out a strict notion of isochores as compositionally homogeneous and that isochores do not appear to deserve the prefix iso . ... 

Since the terminology strict isochores was misleadingly used by the authors to denote sequences that cannot be distinguished from random (uncorrelated) sequences (in which every nucleotide is free to change), their failure to identify in the human genome sequences as homogeneous as random sequences (masquerading as strict isochores ) could have been predicted easily on three accounts. 

Third, strict isochores cannot exist in any natural DNA (i) because coding sequences are made up of codons, in which the compositions of the three positions are correlated with each other (D Onofrio and Bernardi, 1992) (ii) because non-coding sequences are com-positionally correlated with the coding sequences that they embed (Bernardi et al., 1985b Clay et al., 1996 see Chapter 3 below) and (iii) because interspersed repeats are characterized by their own specific sequences. More detailed discussions of this problem were presented by Clay and Bernardi (2001a,b), Clay et al. (2001) and Clay (2001). 

In summary, the conclusion of Lander et al. (2001) that isochores are not strict isochores , i.e. are not as homogeneous as random sequences is correct, but it is something we have known for at least 20 years. To take random sequences as a reference for homogeneity and looking for the same level of homogeneity in human DNA sequences was a mistake. Furthermore, it raised doubts about the very existence of isochores in readers who were not familiar with this issue, and this was unfortunate. 

Around the same time, other laboratories also missed the point that strict isochores cannot exist in natural DNA and also took random sequences as references for compositional homogeneity (Haring and Kypr, 2001 and also, in part, Nekrutenko and Li, 2000 these papers have been commented in detail in Clay and Bernardi 2001a,b Clay et al., 2001). 

Fig. 2.16. Temperature dependences of the dielectric relaxation times for PVAc at atmospheric pressure ( ) and at a constant volume equal to 0.847 mlg (A), 0.849 ml ( ), and 0.852 ml g (V). The slopes at the intersection of the iso-baric and isochoric lines yield values for the respective activation energies at constant pressure and constant volume a = 238 and 448kJmol (r = 2.5 s) and = 166 and 293 kJ mol (r = 0.003 s). The ratio of the isochoric and isobaric activation energies is a measure of the relative contribution of thermal energy and volume that is, this ratio would be unity if the molecular motion were thermally activated, and zero if it were strictly dominated by density. For PVAc, the ratio is 0.6, indicating that both contributions are significant. From Roland and Casalini by permission [132].

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