Protein Folding Simulations: Confinement, External Fields and Sequence Design

The present Thesis looks at the problem of protein folding using Monte Carlo and Langevin simulations, three topics in protein folding have been studied: 1) the effect of confining potential barriers, 2) the effect of a static external field and 3) the design of amino acid sequences which fold in a short time and which have a stable native state (global minimum). Regarding the first topic, we studied the confinement of a small protein of 16 amino acids known as 1NJ0 (PDB code) which has a beta-sheet structure as a native state. The confinement of proteins occurs frequently in the cell environment. Some molecules called Chaperones, present in the cytoplasm, capture the unfolded proteins in their interior and avoid the formation of aggregates and misfolded proteins. This mechanism of confinement mediated by Chaperones is not yet well understood. In the present work we considered two kinds of potential barriers which try to mimic the confinement induced by a Chaperon molecule. The first kind of potential was a purely repulsive barrier whose only effect is to create a cavity where the protein folds up correctly. The second kind of potential was a barrier which includes both attractive and repulsive effects. We performed Wang-Landau simulations to calculate the thermodynamical properties of 1NJ0. From the free energy landscape plot we found that 1NJ0 has two intermediate states in the bulk (without confinement) which are clearly separated from the native and the unfolded states. For the case of the purely repulsive barrier we found that the intermediate states get closer to each other in the free energy landscape plot and eventually they collapse into a single intermediate state. The unfolded state is more compact, compared to that in the bulk, as the size of the barrier decreases. For an attractive barrier modifications of the states (native, unfolded and intermediates) are observed depending on the degree of attraction between the protein and the walls of the barrier. The strength of the attraction is measured by the parameter $\epsilon$. A purely repulsive barrier is obtained for $\epsilon=0$ and a purely attractive barrier for $\epsilon=1$. The states are changed slightly for magnitudes of the attraction up to $\epsilon=0.4$. The disappearance of the intermediate states of 1NJ0 is already observed for $\epsilon =0.6$. A very high attractive barrier ($\epsilon \sim 1.0$) produces a completely denatured state. In the second topic of this Thesis we dealt with the interaction of a protein with an external electric field. We demonstrated by means of computer simulations, specifically by using the Wang-Landau algorithm, that the folded, unfolded, and intermediate states can be modified by means of a field. We have found that an external field can induce several modifications in the thermodynamics of these states: for relatively low magnitudes of the field ($<2.06 \times 10^8$ V/m) no major changes in the states are observed. However, for higher magnitudes than ($6.19 \times 10^8$ V/m) one observes the appearance of a new native state which exhibits a helix-like structure. In contrast, the original native state is a $\beta$-sheet structure. In the new native state all the dipoles in the backbone structure are aligned parallel to the field. The design of amino acid sequences constitutes the third topic of the present work. We have tested the Rate of Convergence criterion proposed by D. Gridnev and M. Garcia ({\it work unpublished}). We applied it to the study of off-lattice models. The Rate of Convergence criterion is used to decide if a certain sequence will fold up correctly within a relatively short time. Before the present work, the common way to decide if a certain sequence was a good/bad folder was by performing the whole dynamics until the sequence got its native state (if it existed), or by studying the curvature of the potential energy surface. There are some difficulties in the last two approaches. In the first approach, performing the complete dynamics for hundreds of sequences is a rather challenging task because of the CPU time needed. In the second approach, calculating the curvature of the potential energy surface is possible only for very smooth surfaces. The Rate of Convergence criterion seems to avoid the previous difficulties. With this criterion one does not need to perform the complete dynamics to find the good and bad sequences. Also, the criterion does not depend on the kind of force field used and therefore it can be used even for very rugged energy surfaces.

The effect of electric field direction on the-shear stress of ER fluids

The effect of the direction of external electric field on the shear stress of an ER fluid has been studied by molecular-dynamics simulation. Due to the formation of inclined chains, the shear stress strongly depends on the direction of the field, and it may be very large under some special field direction. And theoretical model of ideal microstructure of ER fluids has proved this result. Thus the ER effect may be greatly enhanced just by choosing an optimum direction for the field without any additional requirement, suggesting a promising way to the practical application of ER fluids.

Quasinormal modes of black holes immersed in a strong magnetic field

We found quasinormal modes, both in time and frequency domains, of the Ernst black holes, that is neutral black holes immersed in an external magnetic field. The Ernst solution reduces to the Schwarzschild solution, when the magnetic field vanishes. It is found that the quasinormal spectrum for massless scalar field in the vicinity of the magnetized black holes acquires an effective ""mass"" mu = 2B vertical bar m vertical bar, where m is the azimuthal number and B is parameter describing the magnetic field. We shall show that in the presence of a magnetic field quasinormal modes are longer lived and have larger oscillation frequencies. The perturbations of higher-dimensional magnetized black holes by Ortaggio and of magnetized dilaton black holes by Radu are considered. (C) 2007 Elsevier B.V. All rights reserved.

Current distribution and Lorentz field modelling using cathode designs : a parametric approach

A mathematical model of magnetohydrodynamic (MHD) effects in an aluminium cell using numerical approximation of a finite element method is presented. The model predicts the current distribution in the cell and calculates the Lorentz force from the external magnetic field in molten metal for cathode blocks with different surface inclinations.

The findings indicated that the cathode surface inclinations have significant influence on cathode current density and Lorentz field distribution in the molten metal. The results establish a trend for the current density and associated MHD force distributions with increase in cathode inclination angle, φ. It has been found that cathode with φ = 5^o inclination could decrease 16 to 20 % of Lorentz force in the molten metal.

Molecular dynamics study of response of liquid N,N-dimethylformamide to externally applied electric field using a polarizable force field

The behavior of Liquid N,N-dimethylformamide subjected to a wide range of externally applied electric fields (from 0.001 V/nm to 1 V/nm) has been investigated through molecular dynamics simulation. To approach the objective the AMOEBA polarizable force field was extended to include the interaction of the external electric field with atomic partial charges and the contribution to the atomic polarization. The simulation results were evaluated with quantum mechanical calculations. The results from the present force field for the liquid at normal conditions were compared with the experimental and molecular dynamics results with non-polarizable and other polarizable force fields. The uniform external electric fields of higher than 0.01 V/nm have a significant effect on the structure of the liquid, which exhibits a variation in numerous properties, including molecular polarization, local cluster structure, rotation, alignment, energetics, and bulk thermodynamic and structural properties.

Bubble flow in a static magnetic field

A lab-based electrolytic-cell is designed to analyze the effect of external magnetic field on bubble evolution underneath an anode surface. Buckingham Pi theorem is used to provide a complete list of dimensionless parameters for a typical cell configuration. There is an increase in bubble size and the number of bubbles with time. The hydrodynamic convection is apparent due to the effect of electrolyte flow caused by swarm of bubbles rising along the anode surface. The image sequence shows that swarm of bubbles exhibit a swirling flow-field in the presence of the magnetic field. The coalescence process intensifies in an area where magnetic field is higher. As a consequence, bubbles are swept away by the magneto-hydrodynamic (MHD) convection. These results suggest that a magnetic field causes remarkable improvement on the surface coverage of the anode.

Effect of target bias on magnetic field enhanced plasma immersion ion implantation

Recent studies have demonstrated that sheath dynamics in plasma immersion ion implantation (PIII) is significantly affected by an external magnetic field, especially in the case when the magnetic field is parallel to the workpiece surface or intersects it at small angles. In this work we report the results from two-dimensional, particle-in-cell (PIC) computer simulations of magnetic field enhanced plasma immersion implantation system at different bias voltages. The simulations begin with initial low-density nitrogen plasma, which extends with uniform density through a grounded cylindrical chamber. Negative bias voltage is applied to a cylindrical target located on the axis of the vacuum chamber. An axial magnetic field is created by a solenoid installed inside the target holder. A set of simulations at a fixed magnetic field of 0.0025 T at the target surface is performed. Secondary electron emission from the target subjected to ion bombardment is also included. It is found that the plasma density around the cylindrical target increases because of intense background gas ionization by the electrons drifting in the crossed E x B fields. Suppression of the sheath expansion and increase of the implantation current density in front of the high-density plasma region are observed. The effect of target bias on the sheath dynamics and implantation current of the magnetic field enhanced PIII is discussed. (C) 2007 Elsevier B.V. All rights reserved.

Atomic radiative transitions in thermo field dynamics

In this work we rederive the Lamb-Retherford energy shift for an atomic electron in the presence of a thermal radiation. Using the Dalibard, Dupont-Roc and Cohen-Tannoudji (DDC) formalism, where physical observables are expressed as convolutions of suitable statistical functions, we construct the electromagnetic field propagator of thermo field dynamics in the Coulomb gauge in order to investigate finite temperature effects on the atomic energy levels. In the same context, we also analyze the problem of the ground state stability.

Photon mass and gravitational deflection

The deflection of a massive photon by an external gravitational field is energy-dependent. Interesting enough, any massive quantum particle, no matter what its spin is, undergoes dispersive deflection in external gravitational fields. Exploiting the dispersive deflection of the quantized massive electromagnetic radiation by the gravitational field of the Sun, we find an upper bound for the photon mass.

Absorption cross section of electromagnetic waves for Schwarzschild black holes

The absorption cross section of black holes has been investigated for various fields. Nevertheless, the absorption cross section of Schwarzschild black holes for the electromagnetic field has been only calculated in the low- and high-frequency approximations until now. Here we compute it numerically for arbitrary frequencies.

Semiclassical approach to black hole absorption of electromagnetic radiation emitted by a rotating charge

We consider an electric charge, minimally coupled to the Maxwell field, rotating around a Schwarzschild black hole. We investigate how much of the radiation emitted from the swirling charge is absorbed by the black hole and show that most of the photons escape to infinity. For this purpose we use the Gupta-Bleuler quantization of the electromagnetic field in the modified Feynman gauge developed in the context of quantum field theory in Schwarzschild spacetime. We obtain that the two photon polarizations contribute quite differently to the emitted power. In addition, we discuss the accurateness of the results obtained in a full general relativistic approach in comparison with the ones obtained when the electric charge is assumed to be orbiting a massive object due to a Newtonian force.

Electromagnetic energy-momentum and forces in matter

We discuss the electromagnetic energy-momentum distribution and the mechanical forces of the electromagnetic field in material media. There is a long-standing controversy on these notions. The Minkowski and the Abraham energy-momentum tensors are the most well-known ones. We propose a solution of this problem which appears to be natural and self-consistent from both a theoretical and an experimental point of view. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Massless DKP field in a Lyra manifold

Massless scalar and vector fields are coupled to the Lyra geometry by means of the Duffin-Kemmer-Petiau (DKP) theory. Using the Schwinger variational principle, the equations of motion, conservation laws and gauge symmetry are implemented. We find that the scalar field couples to the anholonomic part of the torsion tensor, and the gauge symmetry of the electromagnetic field does not break by the coupling with torsion.

On equivalence of Duffin-Kemmer-Petiau and Klein-Gordon equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical simulation of magnetic-field-enhanced plasma immersion ion implantation in cylindrical geometry

Recent studies have demonstrated that the sheath dynamics in plasma immersion ion implantation (PIII) is significantly affected by an external magnetic field. In this paper, a two-dimensional computer simulation of a magnetic-field-enhanced PHI system is described. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded vacuum chamber filled with uniform molecular nitrogen plasma. A static magnetic field is created by a small coil installed inside the target holder. The vacuum chamber is filled with background nitrogen gas to form a plasma in which collisions of electrons and neutrals are simulated by the Monte Carlo algorithm. It is found that a high-density plasma is formed around the target due to the intense background gas ionization by the magnetized electrons drifting in the crossed E x B fields. The effect of the magnetic field intensity, the target bias, and the gas pressure on the sheath dynamics and implantation current of the PHI system is investigated.