Thermodynamic definition of mean temperature

The notion of mean temperature is crucial for a number of fields, including climate science, fluid dynamics, and biophysics. However, so far its correct thermodynamic foundation is lacking or even believed to be impossible. A physically correct definition should not be based on mathematical notions of the means (e.g., the mean geometric or mean arithmetic), because they are not unique, and they ignore the fact that temperature is an ordinal level variable. We offer a thermodynamic definition of the mean temperature that is based upon the following two assumptions. First, the correct definition should necessarily involve equilibration processes in the initially nonequilibrium system. Among such processes, reversible equilibration and fully irreversible equilibration are the two extreme cases. Second, within the thermodynamic approach we assume that the mean temperature is determined mostly by energy and entropy. Together with the dimensional analysis, the two assumptions lead to a definition of the mean temperature that is determined up to a weight factor that can be fixed to 1/2 due to the maximum ignorance principle. The mean temperature for ideal and (van der Waals) nonideal gases with temperature-independent heat capacity is given by a general and compact formula that (besides the initial temperatures) only depends on the heat capacities and concentration of gases. Our method works for any nonequilibrium initial state, not only two-temperature states.

Thermal-induced force release in oxyhemoglobin

Oxygen is released to living tissues via conformational changes of hemoglobin from R-state (oxyhemoglobin) to T-state (desoxyhemoglobin). The detailed mechanism of this process is not yet fully understood. We have carried out micromechanical experiments on oxyhemoglobin crystals to determine the behavior of the Young’s modulus and the internal friction for temperatures between 20 °C and 70 °C. We have found that around 49 °C oxyhemoglobin crystal samples undergo a sudden and strong increase of their Young’s modulus, accompanied by a sudden decrease of the internal friction. This sudden mechanical change (and the ensuing force release) takes place in a partially unfolded state and precedes the full denaturation transition at higher temperatures. After this transformation, the hemoglobin crystals have the same mechanical properties as their initial state at room temperatures. We conjecture that it can be relevant for explaining the oxygen-releasing function of native oxyhemoglobin when the temperature is increased, e.g. due to active sport. The effect is specific for the quaternary structure of hemoglobin, and is absent for myoglobin with only one peptide sequence.

Thermal (in)stability of type I collagen fibrils

We measured the Young's modulus at temperatures ranging from 20 to 100 degrees C for a collagen fibril that is taken from a rat's tendon. The hydration change under heating and the damping decrement were measured as well. At physiological temperatures 25 to 45 degrees C, the Young's modulus decreases, which can be interpreted as an instability of the collagen. For temperatures between 45 and 80 degrees C, the Young's modulus first stabilizes and then increases when the temperature is increased. The hydrated water content and the damping decrement have strong maximums in the interval 70 to 80 degrees C indicating complex intermolecular structural changes in the fibril. All these effects disappear after heat-denaturation of the sample at 120 degrees C. Our main achievement is a five-stage mechanism by which the instability of a single collagen at physiological temperatures is compensated by the interaction between collagen molecules.

Mechanical properties of DNA films

The Young's dynamical modulus (E) and the DNA film logarithmic decrement (theta) at frequencies from 50 Hz to 20 kHz are measured. These values are investigated as functions of the degree of hydration and temperature. Isotherms of DNA film hydration at 25 degrees C are measured. The process of film hydration changing with temperature is studied. It is shown that the Young's modulus for wet DNA films (E = 0.02-0.025 GN m-2) strongly increases with decreasing hydration and makes E = 0.5-0.7 GN m-2. Dependence of E on hydration is of a complex character. Young's modulus of denatured DNA films is larger than that of native ones. All peculiarities of changing of E and theta of native DNA films (observed at variation of hydration) vanish in the case of denatured ones. The native and denatured DNA films isotherms are different and depend on the technique of denaturation. The Young's modulus of DNA films containing greater than 1 g H2O/g dry DNA is found to decrease with increasing temperature, undergoing a number of step-like changes accompanied by changes in the film hydration. At low water content (less than 0.3 g H2O/g dry DNA), changing of E with increasing temperature takes place smoothly. The denaturation temperature is a function of the water content.

[Relation between the lysozyme hydration isotherm and molecule packing in the solid phase]

A micromethod for measurement of mass changes of glutaraldehyde treated protein crystals is presented. The method is based on analysis of transverse resonance vibration of a cantilevered tungsten micro-needle (1,5 divided by 2 mm long, 30 divided by 40 mkm in diameter) having the specimen stuck on its free sharp end. The method is accurate to within 0.1% for specimens with masses 0.1 divided by 0.01 mg. Absorption isotherms for water uptake by triclinic (P1), monoclinic (P2(1) ) and tetragonal (P4(3)2(1)2) crystals as well as by amorphous films of hen egg-white lysozyme are obtained. Hydration of lysozyme molecule is shown to be highly dependent on molecular packing in the sample both at low and high relative humidities.