Figure 1. The protein folding funnel for a fast-folding helical protein. Copyright Elsevier Cell Press 1996.
While the difference in the Gibbs free energy, ΔG, between the initial and the final thermodynamic equilibrium states of the unfolding/refolding mechanisms has been investigated from both a theoretical and experimental points of view,5 the study of intermediate nonequilibrium states is also important as these states may influence the folding process during biosynthesis and may help understand misfolding, which is the cause of some diseases.6 Thermodynamically, the folding process might occur at constant temperature (the physiological environment is assumed to be a thermal bath) but stochastic nonequilibrium intermediate states may present thermal fluctuations that may be related to energy (heat) exchange between the protein and the physiological environment.7 Therefore, the measurement of those temperature fluctuations/heat exchange is important to better understand the thermodynamics of those intermediate nonequilibrium states and its influence during the (mis)folding process. Besides the folding process, real time temperature measurements would also be appealing for the study of fluctuations due to thermal noise in proteins that work as motors (rotary and linear engines) and shuttles.8 These proteins generally use chemical reactions such as ATP hydrolysis as a fuel to generate mechanical work. Taking into account the first law of thermodynamics, part of the energy received by the protein is converted into useful work and the remaining energy is lost as heat. When proteins help transporting ions/molecules through cell membrane, for example, the work is considered thermodynamically favorable when the transport is performed from a region of high ion/molecule concentration to a region of low ion/molecule concentration. In this case, ΔG is associated to the chemical potential difference and the reversible work needed to perform the transport of ions/molecules across the membrane.9As a transport phenomenon, it may also be viewed as a nonequilibrium thermodynamical process in which heat conduction may lead to gradients of temperature and entropy production with time. Thus, the direct measurement of those temperature gradients may be relevant information to assess and perhaps optimize the efficiency of the energy cycle of the molecular motor.
Protein dynamics: theoretical and experimental analyses
Protein dynamics has been investigated by a number of theoretical methodologies and experimental techniques. From a theoretical point of view, computational and modeling have been using to analyze energy change in protein folding using statistical mechanics and nonequilibrium thermodynamics.10,11 From the experimental point of view, X-ray crystallography, optical spectroscopy, and nuclear magnetic resonance have been commonly used.12 All these experimental techniques are employed in ensembles, i.e., the information retrieved is based on the collective behavior (average) of the objects of study, and therefore individual behavior associated to stochastic nonequilibrium fluctuations are not detectable. Single molecule experiments have been focused on fluorescence correlation spectroscopy to study protein folding as a diffusive process on a free-energy surface13 and optical tweezer/atomic force microscopy to establish mechanical forces to stretch (unfold) the macromolecule and observe the dynamics of the refolding process.14Concerning proteins working as motors and shuttles, experimental techniques such as magnetic tweezers and electrorotation have been used to estimate the thermodynamic efficiency under some constraint conditions such as quasi static limit.15 All the single molecule experiments mentioned here were based on an external stimulus to induce some mechanical motion (folding, rotation) in order to study the dynamics of the system. However, biological systems under external stimulation and without external stimulation may undergo different metabolisms. Nothing has been tried concerning real time temperature measurements on individual proteins spontaneously folding/performing a mechanical work. As mentioned earlier in the text, valuable information about misfolding during biosynthesis and poor engine efficiency, both possibly associated to stochastic thermodynamical nonequilibrium states, may be hypothetically retrieved by measurements of thermal fluctuations and, consequently, estimates of energy related thermodynamic variables. Actually, the study of temperature fluctuations in nonequilibrium thermodynamical phenomena can be more widespread, not restricted only to proteins but it can be extended to other types of biomacromolecules, such as for example DNA. Thus, the potential for using nanothermometers for probing nonequilibrium phenomena in biochemical reactions involving macromolecules is substantial.
Luminescence thermometry in a single protein: the experimental limitations and challenges
Optical temperature sensing using a single luminescent object linked to a biomacromolecule presents many challenges. For accurate real time temperature monitoring of biomacromolecules, the luminescence nanothermometer has to be in contact with the biomacromolecule while the temperature is estimated through some remote detection system that records some change of the luminescence profile with the temperature on the object of study. Imaging and sensing of biological ensemble systems have been accomplished using different classes of luminophores, such as semiconductor quantum dots, lanthanide doped nanocrystals, and fluorescent proteins.16 Inorganic compounds have better photostability, i.e., they do not undergo photodegradation, a characteristic of organic compounds, and therefore they are more convenient for single molecule studies. Due to its lower toxicity level, lanthanide doped nanocrystals are generally more appropriate than semiconductor quantum dots, which contains elements such as Cd, Se and S. However, due to its larger size and constitution, inorganic nanoparticles-biomacromolecules conjugates are much more complicated to fabricate than fluorescent proteins-biomacromolecules conjugates.16 Thermometry using a single fluorescent protein is complicated by the fact that besides photodegradation due to long exposure to light excitation, organic molecules also show blinking, a characteristic of electronic population of dark states during relaxation. Lanthanide doped nanoparticles, on the other hand, do not present blinking because a single nanoparticle has many luminophores, the lanthanide ions. Recent imaging and spectral analysis of the luminescence profile of individual lanthanide doped nanoparticles are available in literature.17,18 Figure 2 shows the luminescence spectral profile of a NaYF4 nanoparticle doped lanthanides (Yb3+ and Er3+). The signal was recorded with a scanning confocal microscopy set-up.17 Observe that the relative intensity of the two emission bands at 520-535 nm and 540-560 nm, which are radiative relaxations from thermally coupled electronic states4S3/2 and2H11/2 of Er3+, changes with the temperature in a way that optical temperature sensing is feasible.