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Protein Heat Capacity: An Anomaly that Maybe Never Was Alan Cooper* School of Chemistry, College of Science and Engineering, Joseph Black Building, University of Glasgow, Glasgow G12 8QQ, U.K.
ABSTRACT Protein unfolding in aqueous solution is usually accompanied by an increase in heat capacity (ΔCp), and this has long been regarded as somewhat anomalous. However, neither the absolute heat capacities (Cp) of folded globular proteins nor the heat capacity increments upon unfolding (ΔCp) are unusual in comparison to values observed for order-disorder (melting) transitions in other organic substances. The consequences for protein stability, including cold denaturation, enthalpy-entropy compensation, and the temperature of maximum stability, may seem counterintuitive but should not be unexpected. Nevertheless, while perhaps not so anomalous as once thought, quantitative interpretation of protein heat capacity and related effects remains a theoretical challenge.
A
round 1757, Joseph Black, a colleague from an earlier era in Glasgow, was puzzled by his observations that certain materials took longer to warm up than others. Ice, water, and various “spiritous liquors” were particularly intriguing, and it is said that “He waited with impatience for the winter” so that he could continue his investigations on heating and cooling.1 (There was no ice house in Glasgow, and refrigeration had not yet been invented, though his professor and mentor, William Cullen, was working on it.) This was no idle pursuit; James Watt, Black's friend and “mathematical instrument maker to the University”, at that time was concerned with improving the efficiency of steam engines. What Black showed was that substances undergoing heat-induced phase transitions ; melting, boiling, and evaporation ; did so without an increase in temperature. This led to the concept of “latent” (i.e., hidden) heat, what we now call heat capacity, in which heat energy is somehow used to do something other than simply raise temperature.
Heat Capacity ; The Basics. As the name implies, heat capacity is a measure of the capacity of any object to take up heat energy. At the molecular level, this heat energy will be distributed among the available degrees of freedom and partitioned into kinetic energies (related to vibrational, rotational, or translational motions) or potential energies (related to changes in interatomic potential energies, bond stretching, bending, breaking, and so forth). It follows that the more ways there are of distributing heat energy in a substance, the higher will be its heat capacity. This roughly explains why liquid water has such a relatively high heat capacity; heat energy is diverted into breaking residual intermolecular hydrogen bonds rather than raising the temperature. Heat capacity is central to fundamental thermodynamics because both the absolute enthalpy (H) and the entropy (S) of any object are integral functions of its heat capacity Z ð1Þ HðT Þ ¼ Hð0Þ þ C p dT Z SðT Þ ¼ Sð0Þ þ
The consequences for protein stability may seem counterintuitive but should not be unexpected.
ð2Þ
where Cp is the heat capacity at constant pressure, T is the absolute temperature, and the integral is taken from absolute zero (0 K) to the required temperature. H(0) and S(0) are the zero-point enthalpy and entropy, respectively. (Equivalent expressions exist for heat capacity at constant volume, Cv. Here, however, we shall normally assume constant pressure because that is what mostly applies. Except for gases, the numerical difference between Cp and Cv is negligible for most practical purposes.) For enthalpy (H=U þ PV, with the internal energy, U, corrected for pressure-volume effects), the physical interpretation
Now, 250 years later, we are still intrigued by this, and the properties of water continue to present fascinating challenges. Much of this has been reflected in the discussions surrounding the heat capacity of proteins and the heat capacity changes that accompany protein transitions and interactions. In what follows, I shall try to present a (mostly personal) view of the current situation in relation to heat capacity effects in protein unfolding and related processes in solution, mainly from a physical chemistry perspective. More comprehensive and authoritative reviews can be found elsewhere.2,3
r 2010 American Chemical Society
ðC p =T Þ dT
Received Date: August 27, 2010 Accepted Date: November 1, 2010 Published on Web Date: November 04, 2010
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DOI: 10.1021/jz1012142 |J. Phys. Chem. Lett. 2010, 1, 3298–3304
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Figure 1. Typical DSC data for the unfolding of a small globular protein (lysozyme) in solution at various pH values.8 The increase in area under each endotherm with higher Tm and the higher heat capacity baselines after the unfolding transitions are both indications of the significant positive ΔCp commonly associated with such processes. (Adapted from ref 8, with permission; protein structure drawn from pdb 1HEW.9)
of eq 1 is straightforward; starting from absolute zero, each increment in temperature, dT, requires addition of heat energy, dQ=Cp dT, with summation up to the required temperature to give the total enthalpy. The entropy relationship, eq 2, is perhaps less intuitive but derives from the Second Law definition of the entropy increment, dS = dQ/T = Cp dT/T. In molecular thermodynamics/statistical mechanics terms, this relates to the number of ways in which heat energy may be distributed within the object. Heat capacity also plays a fundamental role in determining the size of thermodynamic fluctuations in any system. All objects are subject to thermal fluctuations arising from Brownian-motion-like bombardment from surrounding atoms and molecules. For any object of mass m and specific heat cv (heat capacity per unit mass), the mean-square internal energy fluctuations at temperature T are given by ÆδU 2 æ ¼ kB T 2 mcv
Figure 2. Examples of commonly observed heat capacity effects associated with protein unfolding in solution. (A) DSC data for thermal denaturation of yeast phosphoglycerate kinase, illustrating exothermic baseline distortion and heat capacity decrease caused by irreversible precipitation of unfolded protein. (B) Repeat DSC scans of thermal unfolding of lysozyme, showing gradual accumulation of misfolded forms, thought to arise from cis-trans isomerization of proline peptide bonds at high temperature.10 Note how the apparent heat capacities for the less-well-folded forms (below Tm) are higher than those in the original native state.
transition enthalpy and entropy changes at 0 K (or any other convenient reference temperature). Equation 4 is often used in its differential form as a convenient way to estimate ΔCp from the temperature dependence of observed heats of reaction
ð3Þ
ΔC p ¼ DΔH=DT
where kB is the Boltzmann constant. For most everyday objects, these fluctuations are so small (in proportion to the total energy) as to go unnoticed most of the time. However, for much smaller objects, particularly microscopic or mesoscopic systems of the size of protein molecules, these fluctuations are relatively large.4,5 This is why protein structures must be considered as dynamic objects at the molecular level. For any thermodynamic transition (A f B) in which the different states (A, B) have different heat capacities, it follows from eqs 1 and 2 that the enthalpy and entropy changes for the transition will also be temperature-dependent Z ΔHðA f BÞ ¼ H B -H A ¼ ΔHð0Þ þ ΔC p dT ð4Þ
Protein Heat Capacity ; The Experimental Situation. The measurement of heat capacities and heat capacity changes for proteins in dilute (
