Research Article

Mesoscopic irreversible thermodynamics of morphological evolution kinetics of helical conformation in bioproteins ‘DNA’ under the isothermal isobaric conditions

Tarik Omer Ogurtani* and Ersin Emre Oren

Published: 03/11/2020 | Volume 4 - Issue 1 | Pages: 009-019


The morphological evolution kinetics and instabilities of alpha helical peptide 3.613, which involves large amount of stored torsional elastic deformation energy (3-40 eV/molecule), is formulated by the variational method based on the connection between the rates of internal entropy production and the changes in the global Gibbs free energy, assuming that one has isobaric irreversible processes under the isothermal conditions. The present mesoscopic nonequilibrium thermodynamic approach relies on the fact that the global Gibbs free energy of helical conformation involves not only the bulk Gibbs free energy of the amino-acid back bone structure but also the interfacial Gibbs free energy of the enclosing cylindrical shell or the cage associated with the side-wall molecular branches, and their interactions with the immediate surroundings. The proposed variational analysis applied directly on the proposed macro-model has furnished a nonlinear integral equation in terms of the normalized and scaled internal and external variables. This allows us to track down the motion of the total pitch height of the alpha polypeptide along the well-defined trajectories in the displacement-time space, dictated not only by the initial configuration of the helix but also through the gradients of the global Gibbs free energy of the strained helical conformation as the main driving force. In the negative manifold, there is a well-defined region below the dynamic instability regime, in which the helical conformation can evolve towards the nonequilibrium stationary states by expanding, or contracting, depending upon whether the interfacial free energy and/or the applied stress system are below or above the well-defined thresholds level dictated by the initial pitch height. The highest life time may be realized along that trajectory, which follows up the threshold level of the interfacial specific Gibbs free energy, which is gs = -315 erg/cm2. In the upper region of the negative manifold, the helical conformations are driven by the very large applied uniaxial tension or the negative pressure induced by the thermal expansion, in the range of p > 1GPa and/or the strong negative interfacial free energies [3-4 pH] or their combinations, they show strong kinematic instabilities, which can cause not only the accelerated unfolding phenomenon but also cause large extensions that end up with the catastrophic decimations by ruptures and fragmentations. In the positive manifold, the aging behavior of the polypeptide follows up a S-shape path having rather speedy aging behavior compared to the negative manifold, which is separated from by a well-defined boundary, which represents the isochoric path having longest relaxation times, which can be achieved with great stability. Finally, one could attempt to estimate the upper limit of the relaxation time of aging for the modern hominin, from samples of exceptional preservations, relying on the present nonequilibrium theory as well as on the very limited knowledge on the post-mortem DNA and the present pitch heights of the modern hominin, which is found to be about 25,840 yrs, with a life expectation of 451,800 yrs. These figures are very close to those calculated for Neanderthals (SH), which are found to be 31,820 yrs and 499,100 yrs, respectively.

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