Folding protein models with a simple hydrophobic energy function: The fundamental importance of monomer inside/outside segregation

The present study explores a “hydrophobic” energy function for folding simulations of the protein lattice model. The contribution of each monomer to conformational energy is the product of its “hydrophobicity” and the number of contacts it makes, i.e., E(h⃗, c⃗) = −Σi=1N cihi = −(h⃗.c⃗) is the negative scalar product between two vectors in N-dimensional cartesian space: h⃗ = (h1, … , hN), which represents monomer hydrophobicities and is sequence-dependent; and c⃗ = (c1, … , cN), which represents the number of contacts made by each monomer and is conformation-dependent. A simple theoretical analysis shows that restrictions are imposed concomitantly on both sequences and native structures if the stability criterion for protein-like behavior is to be satisfied. Given a conformation with vector c⃗, the best sequence is a vector h⃗ on the direction upon which the projection of c⃗ − c̄⃗ is maximal, where c̄⃗ is the diagonal vector with components equal to c̄, the average number of contacts per monomer in the unfolded state. Best native conformations are suggested to be not maximally compact, as assumed in many studies, but the ones with largest variance of contacts among its monomers, i.e., with monomers tending to occupy completely buried or completely exposed positions. This inside/outside segregation is reflected on an apolar/polar distribution on the corresponding sequence. Monte Carlo simulations in two dimensions corroborate this general scheme. Sequences targeted to conformations with large contact variances folded cooperatively with thermodynamics of a two-state transition. Sequences targeted to maximally compact conformations, which have lower contact variance, were either found to have degenerate ground state or to fold with much lower cooperativity.

Denaturant-induced movement of the transition state of protein folding revealed by high-pressure stopped-flow measurements

The small all-β protein tendamistat folds and unfolds with two-state kinetics. We determined the volume changes associated with the folding process by performing kinetic and equilibrium measurements at variable pressure between 0.1 and 100 MPa (1 to 1,000 bar). GdmCl-induced equilibrium unfolding transitions reveal that the volume of the native state is increased by 41.4 ± 2.0 cm3/mol relative to the unfolded state. This value is virtually independent of denaturant concentration. The use of a high-pressure stopped-flow instrument enabled us to measure the activation volumes for the refolding (ΔVf0‡) and unfolding reaction (ΔVu0‡) over a broad range of GdmCl concentrations. The volume of the transition state is 60% native-like (ΔVf0‡ = 25.0 ± 1.2 cm3/mol) in the absence of denaturant, indicating partial solvent accessibility of the core residues. The volume of the transition state increases linearly with denaturant concentration and exceeds the volume of the native state above 6 M GdmCl. This result argues for a largely desolvated transition state with packing deficiencies at high denaturant concentrations and shows that the structure of the transition state depends strongly on the experimental conditions.

NMR investigation of ferricytochrome c unfolding: Detection of an equilibrium unfolding intermediate and residual structure in the denatured state

Horse ferricytochrome c (cyt c) undergoes exchange of one of its axial heme ligands (Met-80) for one or more non-native ligands under denaturing conditions. We have used 1H NMR spectroscopy to detect two conformations of paramagnetic cyt c with non-native heme ligation through a range of urea concentrations. One non-native form is an equilibrium unfolding intermediate observed under partially denaturing conditions and is attributed to replacement of Met-80 with one or more Lys side chains. The second non-native form, in which the native Met ligand is replaced by a His, is observed under strongly denaturing conditions. Thermodynamic analysis of these data indicates a relatively small ΔG (17 kJ/mol) for the transition from native to the Lys-ligated intermediate and a significantly larger ΔG (47 kJ/mol) for the transition from native to the His-ligated species. Although CD and fluorescence data indicate that the equilibrium unfolding of cyt c is a two-state process, these NMR results implicate an intermediate with His-Lys ligation.

A model for amplification of hair-bundle motion by cyclical binding of Ca2+ to mechanoelectrical-transduction channels

Amplification of auditory stimuli by hair cells augments the sensitivity of the vertebrate inner ear. Cell-body contractions of outer hair cells are thought to mediate amplification in the mammalian cochlea. In vertebrates that lack these cells, and perhaps in mammals as well, active movements of hair bundles may underlie amplification. We have evaluated a mathematical model in which amplification stems from the activity of mechanoelectrical-transduction channels. The intracellular binding of Ca2+ to channels is posited to promote their closure, which increases the tension in gating springs and exerts a negative force on the hair bundle. By enhancing bundle motion, this force partially compensates for viscous damping by cochlear fluids. Linear stability analysis of a six-state kinetic model reveals Hopf bifurcations for parameter values in the physiological range. These bifurcations signal conditions under which the system’s behavior changes from a damped oscillatory response to spontaneous limit-cycle oscillation. By varying the number of stereocilia in a bundle and the rate constant for Ca2+ binding, we calculate bifurcation frequencies spanning the observed range of auditory sensitivity for a representative receptor organ, the chicken’s cochlea. Simulations using prebifurcation parameter values demonstrate frequency-selective amplification with a striking compressive nonlinearity. Because transduction channels occur universally in hair cells, this active-channel model describes a mechanism of auditory amplification potentially applicable across species and hair-cell types.

Dissection of the ion-induced folding of the hammerhead ribozyme using 19F NMR

We have used 19F NMR to analyze the metal ion-induced folding of the hammerhead ribozyme by selective incorporation of 5fluorouridine. We have studied the chemical shift and linewidths of 19F resonances of 5-fluorouridine at the 4 and 7 positions in the ribozyme core as a function of added Mg2+. The data fit well to a simple two-state model whereby the formation of domain 1 is induced by the noncooperative binding of Mg2+ with an association constant in the range of 100 to 500 M−1, depending on the concentration of monovalent ions present. The results are in excellent agreement with data reporting on changes in the global shape of the ribozyme. However, the NMR experiments exploit reporters located in the center of the RNA sections undergoing the folding transitions, thereby allowing the assignment of specific nucleotides to the separate stages. The results define the folding pathway at high resolution and provide a time scale for the first transition in the millisecond range.

Non-Arrhenius kinetics for the loop closure of a DNA hairpin

Intramolecular chain diffusion is an elementary process in the conformational fluctuations of the DNA hairpin-loop. We have studied the temperature and viscosity dependence of a model DNA hairpin-loop by FRET (fluorescence resonance energy transfer) fluctuation spectroscopy (FRETfs). Apparent thermodynamic parameters were obtained by analyzing the correlation amplitude through a two-state model and are consistent with steady-state fluorescence measurements. The kinetics of closing the loop show non-Arrhenius behavior, in agreement with theoretical prediction and other experimental measurements on peptide folding. The fluctuation rates show a fractional power dependence (β = 0.83) on the solution viscosity. A much slower intrachain diffusion coefficient in comparison to that of polypeptides was derived based on the first passage time theory of SSS [Szabo, A., Schulten, K. & Schulten, Z. (1980) J. Chem. Phys. 72, 4350–4357], suggesting that intrachain interactions, especially stacking interaction in the loop, might increase the roughness of the free energy surface of the DNA hairpin-loop.

Thermal unfolding of human high-density apolipoprotein A-1: implications for a lipid-free molten globular state.

Apolipoprotein A-1 (apoA-1) in complex with high-density lipoprotein is critically involved in the transport and metabolism of cholesterol and in the pathogenesis of atherosclerosis. We reexamined the thermal unfolding of lipid-free apoA-1 in low-salt solution at pH approximately 7, by using differential scanning calorimetry and circular dichroism. At protein concentrations <5 mg/ml, thermal unfolding of apoA-1 is resolved as an extended peak (25 degrees C-90 degrees C) that can be largely accounted for by a single reversible non-two-state transition with midpoint Tm 57 +/- 1 degree C, calorimetric enthalpy deltaH(Tm)= 200 +/- 20 kcal/mol (1 kcal = 4.18 kJ), van't Hoff enthalpy deltaHv(Tm) approximately 32.5 kcal/mol, and cooperativity deltaHv(Tm)/deltaH(Tm) approximately 0.16. The enthalpy deltaH(Tm) can be accounted for by melting of the alpha-helical structure that is inferred by CD to constitute approximately 60% of apoA-1 amino acids. Farand near-UV CD spectra reveal noncoincident melting of the secondary and tertiary structural elements and indicate a well-defined secondary structure but a largely melted tertiary structure for apoA-1 at approximately 37 degrees C and pH 7. This suggests a molten globular-like state for lipid-free apoA-1 under near-physiological conditions. Our results suggest that in vivo lipid binding by apoA-1 may be mediated via the molten globular apolipoprotein state in plasma.

Simple model of protein folding kinetics.

A simple model of the kinetics of protein folding is presented. The reaction coordinate is the "correctness" of a configuration compared with the native state. The model has a gap in the energy spectrum, a large configurational entropy, a free energy barrier between folded and partially folded states, and a good thermodynamic folding transition. Folding kinetics is described by a master equation. The folding time is estimated by means of a local thermodynamic equilibrium assumption and then is calculated both numerically and analytically by solving the master equation. The folding time has a maximum near the folding transition temperature and can have a minimum at a lower temperature.

Critical behavior of three-dimensional disordered Potts models with many states

We study the 3D Disordered Potts Model with p = 5 and p = 6. Our numerical simulations (that severely slow down for increasing p) detect a very clear spin glass phase transition. We evaluate the critical exponents and the critical value of the temperature, and we use known results at lower p values to discuss how they evolve for increasing p. We do not find any sign of the presence of a transition to a ferromagnetic regime.

First Order Phase Transition in a 3D disordered system

We present a detailed numerical study on the effects of adding quenched impurities to a three dimensional system which in the pure case undergoes a strong first order phase transition (specifically, the ferromagnetic/paramagnetic transition of the site-diluted four states Potts model). We can state that the transition remains first-order in the presence of quenched disorder (a small amount of it) but it turns out to be second order as more impurities are added. A tricritical point, which is studied by means of Finite-Size Scaling, separates the first-order and second-order parts of the critical line. The results were made possible by a new definition of the disorder average that avoids the diverging-variance probability distributions that arise using the standard methodology. We also made use of a recently proposed microcanonical Monte Carlo method in which entropy, instead of free energy, is the basic quantity.

Real time optimization in chemical process: evaluation of strategies, improvements and industrial application.

The increasing economic competition drives the industry to implement tools that improve their processes efficiencies. The process automation is one of these tools, and the Real Time Optimization (RTO) is an automation methodology that considers economic aspects to update the process control in accordance with market prices and disturbances. Basically, RTO uses a steady-state phenomenological model to predict the process behavior, and then, optimizes an economic objective function subject to this model. Although largely implemented in industry, there is not a general agreement about the benefits of implementing RTO due to some limitations discussed in the present work: structural plant/model mismatch, identifiability issues and low frequency of set points update. Some alternative RTO approaches have been proposed in literature to handle the problem of structural plant/model mismatch. However, there is not a sensible comparison evaluating the scope and limitations of these RTO approaches under different aspects. For this reason, the classical two-step method is compared to more recently derivative-based methods (Modifier Adaptation, Integrated System Optimization and Parameter estimation, and Sufficient Conditions of Feasibility and Optimality) using a Monte Carlo methodology. The results of this comparison show that the classical RTO method is consistent, providing a model flexible enough to represent the process topology, a parameter estimation method appropriate to handle measurement noise characteristics and a method to improve the sample information quality. At each iteration, the RTO methodology updates some key parameter of the model, where it is possible to observe identifiability issues caused by lack of measurements and measurement noise, resulting in bad prediction ability. Therefore, four different parameter estimation approaches (Rotational Discrimination, Automatic Selection and Parameter estimation, Reparametrization via Differential Geometry and classical nonlinear Least Square) are evaluated with respect to their prediction accuracy, robustness and speed. The results show that the Rotational Discrimination method is the most suitable to be implemented in a RTO framework, since it requires less a priori information, it is simple to be implemented and avoid the overfitting caused by the Least Square method. The third RTO drawback discussed in the present thesis is the low frequency of set points update, this problem increases the period in which the process operates at suboptimum conditions. An alternative to handle this problem is proposed in this thesis, by integrating the classic RTO and Self-Optimizing control (SOC) using a new Model Predictive Control strategy. The new approach demonstrates that it is possible to reduce the problem of low frequency of set points updates, improving the economic performance. Finally, the practical aspects of the RTO implementation are carried out in an industrial case study, a Vapor Recompression Distillation (VRD) process located in Paulínea refinery from Petrobras. The conclusions of this study suggest that the model parameters are successfully estimated by the Rotational Discrimination method; the RTO is able to improve the process profit in about 3%, equivalent to 2 million dollars per year; and the integration of SOC and RTO may be an interesting control alternative for the VRD process.

Polarimetric SAR model for soil moisture estimation over vineyards at C-band

In this paper we propose a two-component polarimetric model for soil moisture estimation on vineyards suited for C-band radar data. According to a polarimetric analysis carried out here, this scenario is made up of one dominant direct return from the soil and a multiple scattering component accounting for disturbing and nonmodeled signal fluctuations from soil and short vegetation. We propose a combined X-Bragg/Fresnel approach to characterize the polarized direct response from soil. A validation of this polarimetric model has been performed in terms of its consistency with respect to the available data both from RADARSAT-2 and from indoor measurements. High inversion rates are reported for different phenological stages of vines, and the model gives a consistent interpretation of the data as long as the volume component power remains about or below 50% of the surface contribution power. However, the scarcity of soil moisture measurements in this study prevents the validation of the algorithm in terms of the accuracy of soil moisture retrieval and an extensive campaign is required to fully demonstrate the validity of the model. Different sources of mismatches between the model and the data have been also discussed and analyzed.

Strategy-proof choice of acts : a preliminary study

We model social choices as acts mapping states of the world to (social) outcomes. A (social choice) rule assigns an act to every profile of subjective expected utility preferences over acts. A rule is strategy-proof if no agent ever has an incentive to misrepresent her beliefs about the world or her valuation of the outcomes; it is ex-post efficient if the act selected at any given preference profile picks a Pareto-efficient outcome in every state of the world. We show that every two-agent ex-post efficient and strategy-proof rule is a top selection: the chosen act picks the most preferred outcome of some (possibly different) agent in every state of the world. The states in which an agent’s top outcome is selected cannot vary with the reported valuations of the outcomes but may change with the reported beliefs. We give a complete characterization of the ex-post efficient and strategy-proof rules in the two-agent, two-state case, and we identify a rich class of such rules in the two-agent case.

Trade policy in a dynamic Heckscher-Ohlin model

The Import Substitution Process in Latin Amer ica was an attempt to enhance GDP growth and productivity by rising trade barriers upon capital-intensive products. Our main goal is to analyze how an increase in import tariff on a particular type of good affects the production choices and trade pattern of an economy. We develop an extension of the dynamic Heckscher-Ohlin model – a combination of a static two goods, two-factor Heckscher-Ohlin model and a two-sector growth model – allowing for import tariff. We then calibrate the closed economy model to the US. The results show that the economy will produce less of both consumption and investment goods under autarky for low and high levels of capital stock per worker. We also find that total GDP may be lower under free trade in comparison to autarky.

Strategy-proof choice of acts : a preliminary study

We model social choices as acts mapping states of the world to (social) outcomes. A (social choice) rule assigns an act to every profile of subjective expected utility preferences over acts. A rule is strategy-proof if no agent ever has an incentive to misrepresent her beliefs about the world or her valuation of the outcomes; it is ex-post efficient if the act selected at any given preference profile picks a Pareto-efficient outcome in every state of the world. We show that every two-agent ex-post efficient and strategy-proof rule is a top selection: the chosen act picks the most preferred outcome of some (possibly different) agent in every state of the world. The states in which an agent’s top outcome is selected cannot vary with the reported valuations of the outcomes but may change with the reported beliefs. We give a complete characterization of the ex-post efficient and strategy-proof rules in the two-agent, two-state case, and we identify a rich class of such rules in the two-agent case.