Changes in Heat Capacity by Folding Proteins?

YOUNGWOOD, Pa. - Nov. 29, 2013 - PRLog -- Introduction
Historically, the laws of thermodynamics are formulated on relationships among quantities of free energy G, enthalpy H, and entropy S. Whether a system may proceed from one state to another has been shown to depend on changes ΔG, ΔH, and ΔS.

Over the past 30 years, biological experiments of proteins have contrarily shown  the laws of thermodynamics need revision to include the heat capacity Cp of proteins as a thermodynamic quantity based on changes ΔCp measured between unfolded and folded configurations. In the thumbnail, the heat capacity is depicted to increase as the protein conformation changes from folded to unfolded. More recently, the ΔCp data has even been suggested to correlate with the exposed surface area of proteins during a biological reaction. See PR at http://scienceblogs.com/worldsfair/2010/09/24/heat-capaci... (http://scienceblogs.com/worldsfair/2010/09/24/heat-capacity-in-biology-101-w/)

Generally, DSC is the accepted method [1] to obtain experimental ΔCp data between folding and unfolding states of proteins. DSC stands for differential scanning calorimetry. In DSC, the heat Q supplied to a sample protein and solvent in an open or covered pan at a given temperature is measured and compared to that of a reference of solvent only at the same temperature.

Classical Physics and Quantum Mechanics
DSC assumes the heat Q absorbed by the protein increases its temperature consistent with classical physics that allows the atom to always have heat capacity. However, by QM the protein lacks the heat capacity to conserve Q by an increase in temperature. QM stands for quantum mechanics. By the Einstein-Hopf relation for the atoms in the protein as harmonic oscillators, the heat capacity vanishes for both folded and unfolded conformations. Lacking heat capacity, the heat Q is therefore conserved by QED inducing the protein to emit EM radiation. QED stands for quantum electrodynamics and EM for electromagnetic See QED Applications at http://www.nanoqed.org/ , 2009 – 2014.

Problem
The DSC experiments show the protein has higher heat capacity in the unfolded state than when folded. However, QM in the harmonic region requires the heat capacity of the protein at ambient temperature to vanish at conformations having frequencies higher than the near IR. Heat capacities in the far IR anharmonic region do not vanish, but protein conformations typically vary only from the IR to the UV.

The problem is the DSC assumes the protein follows classical physics in conserving heat Q and increases in temperature, while instead the protein lacking heat capacity follows QM and emits QED induced EM radiation.

Frequency of QED Radiation
The QED Induced EM emission frequencies in the folded and unfolded states differ as noted in the thumbnail. In the unfolded state, the EM emissions are primarily bending and stretching vibrations in the IR; whereas, in the folded state the conformation approaches a continuum that under TIR confinement has electronic resonances in the UV.TIR stands for total internal reflection. Interestingly, the UV based on A230 is used as a structural probe of monitoring [2] protein unfolding. A230 stands for UV absorbance at 230 nm.

DSC and the QED Mechanism
In the DSC, QM by requiring a vanishing heat capacity denies the atom the conservation of heat Q by an increase in temperature. Regardless of conformation, the heat capacity of the protein from the IR to the UV must vanish by QM. Hence, the folded and unfolded heat capacities ΔCp = CpU - CpF = 0.

1. Folded The heat Q absorbed does not increase the temperature because in the folded state the protein is a compact and nearly spherical shape having a high TIR resonance in the UV. Heat Q is therefore converted by QED to non-thermal UV radiation from 230 to 280 nm consistent with the A230 absorbance probe. But the water solvent is transparent in the UV-VIS window, and therefore the water temperature does not increase as heat Q is not absorbed. The DSC therefore shows the heat capacity Cp is lowest in the folded state.

2. Unfolded As the protein unfolds, the conformation frequencies gradually decrease from UV to the IR. Because of the high absorption of water in the IR, the heat Q is promptly conserved by increasing the temperature of the water consistent with the unfolded state having the highest heat capacity.

Open and Covered Samples
Whether the protein sample is covered or not may affect the DSC measurement of heat capacity. In the unfolded protein, the IR is promptly absorbed in the water, and therefore the DSC measures the correct temperature change irrespective of whether the sample is or is not covered. The folded protein differs in that the UV passes through the VIS-UV window of water without increasing the water temperature. Open samples allow the QED induced UV emission to be directly lost to the surroundings, thereby giving a lower heat capacity for the folded protein. But even if the sample is covered, the UV heats the cover and by convection the heat is still lost to the surroundings - the same as for the uncovered sample. Either way, the DSC measures a lower heat capacity for folded than for unfolded proteins when in fact there is no difference in heat capacity as both vanish by QM.

Conclusions

1. Provided protein conformation frequencies are higher than the near IR, QM requires the heat capacity of the protein to vanish. The notion a protein has heat capacity is one from statistical mechanics based on large numbers of molecules, but is not applicable to the heat capacity of individual proteins undergoing conformational changes.

2. The DSC measures ΔCp = CpU – CpF > 0 because the unfolded protein emits in the IR that is absorbed and increases the temperature of the water while the folded protein emits in the VIS-UV window which does not increase the water temperature.

3. Protein folding monitored by UV absorbance at 230 nm is consistent with TIR increasing the frequency of the folded proteins compared to the IR emissions of unfolded conformations.

4. Correlations of ΔCp with the surface area in the unfolded protein that is buried inside the folded protein have no meaning as the heat capacities vanish for all conformations having frequencies higher than the near IR.

5. Thermodynamics should not be revised for biological systems. Heat capacity Cp cannot be a thermodynamic quantity for proteins as it vanishes between folded and unfolded conformations.

References
[1] “MicroCal VP-Capillary DSC system,” http://www.gelifesciences.com/gehcls_images/GELS/Related%... (http://www.gelifesciences.com/gehcls_images/GELS/Related%...)
[2] P. F. Liu, et al., "Revisiting absorbance at 230 nm as a protein unfolding probe," Analytical Biochemistry, 389 (2009) 165–170