Free energy for protein folding from nonequilibrium simulations using the Jarzynski equality

The equilibrium free energy difference between two long-lived molecular species or "conformational states" of a protein (or any other molecule) can in principle be estimated by measuring the work needed to shuttle the system between them, independent of the irreversibility of the process. This is the meaning of the Jarzynski equality (JE), which we test in this paper by performing simulations that unfold a protein by pulling two atoms apart. Pulling is performed fast relative to the relaxation time of the molecule and is thus far from equilibrium. Choosing a simple protein model for which we can independently compute its equilibrium properties, we show that the free energy can be exactly and effectively estimated from nonequilibrium simulations. To do so, one must carefully and correctly determine the ensemble of states that are pulled, which is more important the farther from equilibrium one performs simulations; this highlights a potential problem in using the JE to extract the free energy from forced unfolding experiments. The results presented here also demonstrate that the free energy difference between the native and denatured states of a protein measured in solution is not always equal to the free energy profile that can be estimated from forced unfolding simulations (or experiments) using the JE.     

Direct spectroscopic evidence for competition between thermal molecular agitation and magnetic field in a tetrameric protein in aqueous solution

Samples of a typical tetrameric protein, the hemoglobin, at the concentration of 150 mg/ml in bidistilled water solution, were exposed to a uniform magnetic field at 200 mT at different temperatures of ${15}^{°}\text{C}$, ${40}^{°}\text{C}$ and ${65}^{°}\text{C}$. Fourier Transform Infrared Spectroscopy was used to analyze the response of the secondary structure of the protein to both stress agents, heating and static magnetic field. The most relevant result which was observed was the significant increasing in intensity of the Amide I band after exposure to the uniform magnetic field at the room temperature of ${15}^{°}\text{C}$. This result can be explained assuming that protein's α-helices aligned along the direction of the applied magnetic field due to their large dipole moment, inducing the alignment of the entire protein. Increasing of temperature up to ${40}^{°}\text{C}$ and ${65}^{°}\text{C}$ induced a significant reduction of the increasing in intensity of the Amide I band. This effect may be easily explained assuming that Brownian motion of the protein in water solution caused by thermal molecular agitation increased with increasing of temperature, contrasting the effect of the torque of the magnetic field applied to the protein in water solution.     

Non-Thermal Effects of Microwave Oven Heating on Ground Beef Meat Studied in the Mid-Infrared Region by Fourier Transform Infrared Spectroscopy

The effects of cooking by microwave oven on the secondary structure of lipid and protein contents in bovine ground beef were investigated in the midinfrared region by Fourier transform infrared (FTIR) spectroscopy to highlight the nonthermal effects of microwave oven heating. Samples of bovine ground beef were cooked in a conventional electric oven at the temperature of 175°C for 15 min and in a microwave oven at 800 W for 1½ min. Spectra analyses of bovine meat after cooking in the conventional oven evidenced a relevant increase in intensity of the carbonyl band at 1742 cm^?1 and of the methylene group at 2921 and 2853 cm^?1 that can be attributed to the Maillard reaction. In contrast, the increase in intensity of these bands after microwave oven heating was less than that which occurred after conventional cooking, showing that the temperature in ground beef meat samples during microwave heating was less than that induced by conventional heating. Spectral analysis in the amide I, II, and III regions showed that a significant increase in intensity occurred in the region from 1660 to 1675 cm^?1 and around 1695, 1635, 1575, and 988 cm^?1 after cooking by means of a microwave oven. These features, which can be attributed to β-turns and β-sheet structures, are characteristic of disorder processes in meat protein contents and increasing transition dipole coupling due to higher contents in aggregated β-sheet structures. This result highlighted nonthermal effects of microwave oven heating in the protein's secondary structure.     

Foundations for a Theory of Complex Matroids

We explore a combinatorial theory of linear dependency in complex space, complex matroids, with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of complex matroids, showing that this theory captures properties of linear dependency, orthogonality, and determinants over ? in much the same way that oriented matroids capture the same properties over ?. In addition, our complex matroids come with a canonical S ¹ action analogous to the action of ?^? on a complex vector space. Our phirotopes (analogs of determinants) are the same as those studied previously by Below, Krummeck, and Richter-Gebert (Discrete and Computational Geometry, Springer, pp.?203?C233, 2003) and Delucchi (Diploma Thesis, ETH Zurich, 2003). We further show that complex matroids cannot have vector axioms analogous to those for oriented matroids.     

Metriplectic framework for dissipative magneto-hydrodynamics

The metriplectic framework, which allows for the formulation of an algebraic structure for dissipative systems, is applied to visco-resistive Magneto-Hydrodynamics (MHD), adapting what had already been done for non-ideal Hydrodynamics (HD). The result is obtained by extending the HD symmetric bracket and free energy to include magnetic field dynamics and resistive dissipation. The correct equations of motion are obtained once one of the Casimirs of the Poisson bracket for ideal MHD is identified with the total thermodynamic entropy of the plasma. The metriplectic framework of MHD is shown to be invariant under the Galileo Group. The metriplectic structure also permits us to obtain the asymptotic equilibria toward which the dynamics of the system evolves. This scheme is finally adapted to the two-dimensional incompressible resistive MHD, that is of major use in many applications.