Frequency spectrum of enthalpy fluctuations associated with macromolecular transitions

General relations to obtain the time-dependent heat capacity from isothermal simulations

It is well-known that time-dependent correlation functions related to temperature and energy can crucially depend on the thermostatting mechanism used in computer simulations of molecular systems. We argue, however, that linear response functions must be considered as universal properties of physical systems. This implies that the classical fluctuation equation for the transient heat capacity, c_v(t), is not applicable to the thermostatted molecular dynamics (apart from long enough times). To improve on this point, we derive a number of exact general expressions for the frequency-dependent heat capacity in terms of energy correlation functions, valid for the Nosé-Hoover and some other thermostats. We also establish a general relation between auto- and cross correlation functions of energy and temperature. Recommendations on how to use these relations to maximize the numerical precision are provided. It is demonstrated that our approach allows us to obtain c_v(t) for a supercooled liquid system with high precision and over many decades in time reflecting all pertinent relaxation processes.

Identification of two-step chemical mechanisms using small temperature oscillations and a single tagged species

In order to identify two-step chemical mechanisms, we propose a method based on a small temperature modulation and on the analysis of the concentration oscillations of a single tagged species involved in the first step. The thermokinetic parameters of the first reaction step are first determined. Then, we build test functions that are constant only if the chemical system actually possesses some assumed two-step mechanism. Next, if the test functions plotted using experimental data are actually even, the mechanism is attributed and the obtained constant values provide the rate constants and enthalpy of reaction of the second step. The advantage of the protocol is to use the first step as a probe reaction to reveal the dynamics of the second step, which can hence be relieved of any tagging. The protocol is anticipated to apply to many mechanisms of biological relevance. As far as ligand binding is considered, our approach can address receptor conformational changes or dimerization as well as competition with or modulation by a second partner. The method can also be used to screen libraries of untagged compounds, relying on a tracer whose concentration can be spectroscopically monitored.

Relaxation dynamics of the gel to liquid-crystalline transition of phosphatidylcholine bilayers. Effects of chainlength and vesicle size

The relaxation kinetics of the gel to liquid-crystalline transition of five phosphatidylcholine (DC14PC to DC18PC) bilayer dispersions have been investigated using volume perturbation calorimetry, a steady-state technique which subjects a sample to sinusoidal changes in volume. Temperature and pressure responses to the volume perturbation are measured to monitor the relaxation to a new equilibrium position. The amplitude demodulation and phase shift of these observables are analyzed with respect to the perturbation frequency to yield relaxation times and amplitudes. In the limit of low perturbation frequency, the temperature and pressure responses are proportional to the equilibrium excess heat capacity and bulk modulus, respectively. At all temperatures, the thermal response data are consistent with a single primary relaxation process of the lipid. The less accurate bulk modulus data exhibit two relaxation times, but it is not clear whether they reflect lipid processes or are characteristic of the instrument. The observed thermal relaxation behavior of all multilamellar vesicles are quantitatively similar. The relaxation times vary from approximately 50 ms to 4 s, with a pronounced maximum at a temperature just greater than Tm, the temperature of the excess heat capacity maximum. Large unilamellar vesicles also exhibit a single relaxation process, but without a pronounced maximum in the relaxation time. Their relaxation time is approximately 80 ms over most of the transition range.

Multifrequency calorimetry of the folding/unfolding transition of cytochrome c

The folding-unfolding transition of Fe(III) cytochrome c has been studied with the new technique of multifrequency calorimetry. Multifrequency calorimetry is aimed at measuring directly the dynamics of the energetic events that take place during a thermally induced transition by measuring the frequency dispersion of the heat capacity. This is done by modulating the folding/unfolding equilibrium using a variable frequency, small oscillatory temperature perturbation (approximately 0.05-0.1 degrees C) centered at the equilibrium temperature of the system. Fe(III) cytochrome c at pH 4 undergoes a fully reversible folding/unfolding transition centered at 67.7 degrees C and characterized by an enthalpy change of 81 kcal/mol and heat capacity difference between unfolded and folded states of 0.9 kcal/K*mol. By measuring the temperature dependence of the frequency dispersion of the heat capacity in the frequency range of 0.1-1 Hz it has been possible to examine the time regime of the enthalpic events associated with the transition. The multifrequency calorimetry results indicate that approximately 85% of the excess heat capacity associated with the folding/unfolding transition relaxes with a single relaxation time of 326 +/- 68 ms at the midpoint of the transition region. This is the first time that the time regime in which heat is absorbed and released during protein folding/unfolding has been measured.