Statistical properties of contact vectors

We study the statistical properties of contact vectors, a construct to characterize a protein's structure. The contact vector of an N-residue protein is a list of N integers n_i, representing the number of residues in contact with residue i. We study analytically (at mean-field level) and numerically the amount of structural information contained in a contact vector. Analytical calculations reveal that a large variance in the contact numbers reduces the degeneracy of the mapping between contact vectors and structures. Exact enumeration for lengths up to N=16 on the three dimensional cubic lattice indicates that the growth rate of number of contact vectors as a function of N is only 3% less than that for contact maps. In particular, for compact structures we present numerical evidence that, practically, each contact vector corresponds to only a handful of structures. We discuss how this information can be used for better structure prediction.Comment: 20 pages, 6 figure

Protein folding using contact maps

We present the development of the idea to use dynamics in the space of contact maps as a computational approach to the protein folding problem. We first introduce two important technical ingredients, the reconstruction of a three dimensional conformation from a contact map and the Monte Carlo dynamics in contact map space. We then discuss two approximations to the free energy of the contact maps and a method to derive energy parameters based on perceptron learning. Finally we present results, first for predictions based on threading and then for energy minimization of crambin and of a set of 6 immunoglobulins. The main result is that we proved that the two simple approximations we studied for the free energy are not suitable for protein folding. Perspectives are discussed in the last section.Comment: 29 pages, 10 figure

The Origin of the Designability of Protein Structures

We examined what determines the designability of 2-letter codes (H and P) lattice proteins from three points of view. First, whether the native structure is searched within all possible structures or within maximally compact structures. Second, whether the structure of the used lattice is bipartite or not. Third, the effect of the length of the chain, namely, the number of monomers on the chain. We found that the bipartiteness of the lattice structure is not a main factor which determines the designability. Our results suggest that highly designable structures will be found when the length of the chain is sufficiently long to make the hydrophobic core consisting of enough number of monomers.Comment: 17 pages, 2 figure

Produtividade e características agronômicas de Brachiaria brizantha cv. Paiaguás submetida a doses de nitrogênio sob cortes

Objetivou-se descrever a resposta da Brachiaria brizantha cv. Paiaguás em doses de adubação nitrogenada no segundo ano de produção. O experimento foi conduzido na área experimental da Universidade do Estado de Mato Grosso, localizada no município de Tangará da Serra, em blocos casualizados, com seis tratamentos (doses de 0, 50, 100, 150, 200 e 250 kg/ha de N) e quatro repetições, em parcelas de 9 m2 cada. As doses foram parceladas em quatro vezes, aplicadas após cada corte. Observou-se efeito significativo (P ≤ 0,05) para as variáveis alturas de plantas, número de perfilhos/m2, porcentagem de matéria seca, massa verde/ha, massa seca/ha, massa seca de folhas e massa seca de colmos/ha. Os resultados mostram que em doses de 250 kg/ha de N, com condições climáticas favoráveis ao crescimento da forragem há efeito positivo do N sobre o número de perfilhos/m2, a massa seca/ha, a massa seca de folhas e a massa seca de colmos/ha de Brachiaria brizantha cv. Paiaguás

Inhibition of protein crystallization by evolutionary negative design

In this perspective we address the question: why are proteins seemingly so hard to crystallize? We suggest that this is because of evolutionary negative design, i.e. proteins have evolved not to crystallize, because crystallization, as with any type of protein aggregation, compromises the viability of the cell. There is much evidence in the literature that supports this hypothesis, including the effect of mutations on the crystallizability of a protein, the correlations found in the properties of crystal contacts in bioinformatics databases, and the positive use of protein crystallization by bacteria and viruses.Comment: 5 page

Critical Casimir effect in films for generic non-symmetry-breaking boundary conditions

Systems described by an O(n) symmetrical $\phi^4$ Hamiltonian are considered in a $d$-dimensional film geometry at their bulk critical points. A detailed renormalization-group (RG) study of the critical Casimir forces induced between the film's boundary planes by thermal fluctuations is presented for the case where the O(n) symmetry remains unbroken by the surfaces. The boundary planes are assumed to cause short-ranged disturbances of the interactions that can be modelled by standard surface contributions $\propto \bm{\phi}^2$ corresponding to subcritical or critical enhancement of the surface interactions. This translates into mesoscopic boundary conditions of the generic symmetry-preserving Robin type $\partial_n\bm{\phi}=\mathring{c}_j\bm{\phi}$. RG-improved perturbation theory and Abel-Plana techniques are used to compute the $L$-dependent part $f_{\mathrm{res}}$ of the reduced excess free energy per film area $A\to\infty$ to two-loop order. When $d<4$, it takes the scaling form $f_{\mathrm{res}}\approx D(c_1L^{\Phi/\nu},c_2L^{\Phi/\nu})/L^{d-1}$ as $L\to\infty$, where $c_i$ are scaling fields associated with the surface-enhancement variables $\mathring{c}_i$, while $\Phi$ is a standard surface crossover exponent. The scaling function $D(\mathsf{c}_1,\mathsf{c}_2)$ and its analogue $\mathcal{D}(\mathsf{c}_1,\mathsf{c}_2)$ for the Casimir force are determined via expansion in $\epsilon=4-d$ and extrapolated to $d=3$ dimensions. In the special case $\mathsf{c}_1=\mathsf{c}_2=0$, the expansion becomes fractional. Consistency with the known fractional expansions of D(0,0) and $\mathcal{D}(0,0)$ to order $\epsilon^{3/2}$ is achieved by appropriate reorganisation of RG-improved perturbation theory. For appropriate choices of $c_1$ and $c_2$, the Casimir forces can have either sign. Furthermore, crossovers from attraction to repulsion and vice versa may occur as $L$ increases.Comment: Latex source file, 40 pages, 9 figure

Simulation, Experiment, and Evolution: Understanding Nucleation in Protein S6 Folding

In this study, we explore nucleation and the transition state ensemble of the ribosomal protein S6 using a Monte Carlo Go model in conjunction with restraints from experiment. The results are analyzed in the context of extensive experimental and evolutionary data. The roles of individual residues in the folding nucleus are identified and the order of events in the S6 folding mechanism is explored in detail. Interpretation of our results agrees with, and extends the utility of, experiments that shift f-values by modulating denaturant concentration and presents strong evidence for the realism of the mechanistic details in our Monte Carlo Go model and the structural interpretation of experimental f-values. We also observe plasticity in the contacts of the hydrophobic core that support the specific nucleus. For S6, which binds to RNA and protein after folding, this plasticity may result from the conformational flexibility required to achieve biological function. These results present a theoretical and conceptual picture that is relevant in understanding the mechanism of nucleation in protein folding.Comment: PNAS in pres

Lack of self-averaging in neutral evolution of proteins

We simulate neutral evolution of proteins imposing conservation of the thermodynamic stability of the native state in the framework of an effective model of folding thermodynamics. This procedure generates evolutionary trajectories in sequence space which share two universal features for all of the examined proteins. First, the number of neutral mutations fluctuates broadly from one sequence to another, leading to a non-Poissonian substitution process. Second, the number of neutral mutations displays strong correlations along the trajectory, thus causing the breakdown of self-averaging of the resulting evolutionary substitution process.Comment: 4 pages, 2 figure

Osmotic Dehydration as a Tool for Insdustrialization of Jabuticaba Peel (Myrciaria jabuticaba)

This study evaluated the osmotic dehydration of jabuticaba peel for use as a by-product, with development of new food products. Response surface methodology was used, considering temperature and sucrose concentration as independent variables, assessing their effects on water loss, solid gain, mass loss, and solid gain rate. Sucrose concentration had a greater influence on osmotic process. Temperature increase is necessary in osmotic dehydration, once it leads to tissue softening, which is essential for dehydration of jabuticaba peel. Therefore, the best osmotic dehydration conditions were set at 60°C and 70 °Brix. With respect to the physicochemical characterization of the bioactive compounds of dehydrated jabuticaba peel, considerable amounts of sugars, anthocyanins, and phenolic compounds were observed, besides the antioxidant potential. Thus, dehydration of jabuticaba peel is a viable alternative to minimize the waste generated during harvest, being a product with high nutritional value

Modeling study on the validity of a possibly simplified representation of proteins

The folding characteristics of sequences reduced with a possibly simplified representation of five types of residues are shown to be similar to their original ones with the natural set of residues (20 types or 20 letters). The reduced sequences have a good foldability and fold to the same native structure of their optimized original ones. A large ground state gap for the native structure shows the thermodynamic stability of the reduced sequences. The general validity of such a five-letter reduction is further studied via the correlation between the reduced sequences and the original ones. As a comparison, a reduction with two letters is found not to reproduce the native structure of the original sequences due to its homopolymeric features.Comment: 6 pages with 4 figure