A Program for Fractal and Multifractal Analysis of Two-Dimensional Binary Images. Computer Algorithms versus Mathematical Theory.

In this paper we present a tool to carry out the multifractal analysis of binary, two-dimensional images through the calculation of the Rényi D(q) dimensions and associated statistical regressions. The estimation of a (mono)fractal dimension corresponds to the special case where the moment order is q = 0.

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

Robust regression applied to fractal/multifractal analysis.

Fractal and multifractal are concepts that have grown increasingly popular in recent years in the soil analysis, along with the development of fractal models. One of the common steps is to calculate the slope of a linear fit commonly using least squares method. This shouldn?t be a special problem, however, in many situations using experimental data the researcher has to select the range of scales at which is going to work neglecting the rest of points to achieve the best linearity that in this type of analysis is necessary. Robust regression is a form of regression analysis designed to circumvent some limitations of traditional parametric and non-parametric methods. In this method we don?t have to assume that the outlier point is simply an extreme observation drawn from the tail of a normal distribution not compromising the validity of the regression results. In this work we have evaluated the capacity of robust regression to select the points in the experimental data used trying to avoid subjective choices. Based on this analysis we have developed a new work methodology that implies two basic steps: ? Evaluation of the improvement of linear fitting when consecutive points are eliminated based on R pvalue. In this way we consider the implications of reducing the number of points. ? Evaluation of the significance of slope difference between fitting with the two extremes points and fitted with the available points. We compare the results applying this methodology and the common used least squares one. The data selected for these comparisons are coming from experimental soil roughness transect and simulated based on middle point displacement method adding tendencies and noise. The results are discussed indicating the advantages and disadvantages of each methodology.

On the reaction mechanism of l-lactate oxidase: Quantitative structure-activity analysis of the reaction with para-substituted l-mandelates

The rate constants for reduction of the flavoenzyme, l-lactate oxidase, and a mutant (in which alanine 95 is replaced by glycine), by a series of para-substituted mandelates, in both the 2-1H- and 2-2H- forms, have been measured by rapid reaction spectrophotometry. In all cases, significant isotope effects (1H/2H = 3–7) on the rate constants of flavin reduction were found, indicating that flavin reduction is a direct measure of α-C-H bond breakage. The rate constants show only a small influence of the electronic characteristics of the substituents, but show a good correlation when combined with some substituent volume parameters. A surprisingly good correlation is found with the molecular mass of the substrate. The results are compatible with any mechanism in which there is little development of charge in the transition state. This could be a transfer of hydride to the flavin N(5) position or a synchronous mechanism in which the α-C-H is formally abstracted as a H+ while the resulting charge is simultaneously neutralized by another event.

A link between protein structure and enzyme catalyzed hydrogen tunneling

We present evidence that the size of an active site side chain may modulate the degree of hydrogen tunneling in an enzyme-catalyzed reaction. Primary and secondary kH/kT and kD/kT kinetic isotope effects have been measured for the oxidation of benzyl alcohol catalyzed by horse liver alcohol dehydrogenase at 25°C. As reported in earlier studies, the relationship between secondary kH/kT and kD/kT isotope effects provides a sensitive probe for deviations from classical behavior. In the present work, catalytic efficiency and the extent of hydrogen tunneling have been correlated for the alcohol dehydrogenase-catalyzed hydride transfer among a group of site-directed mutants at position 203. Val-203 interacts with the opposite face of the cofactor NAD+ from the alcohol substrate. The reduction in size of this residue is correlated with diminished tunneling and a two orders of magnitude decrease in catalytic efficiency. Comparison of the x-ray crystal structures of a ternary complex of a high-tunneling (Phe-93 → Trp) and a low-tunneling (Val-203 → Ala) mutant provides a structural basis for the observed effects, demonstrating an increase in the hydrogen transfer distance for the low-tunneling mutant. The Val-203 → Ala ternary complex crystal structure also shows a hyperclosed interdomain geometry relative to the wild-type and the Phe-93 → Trp mutant ternary complex structures. This demonstrates a flexibility in interdomain movement that could potentially narrow the distance between the donor and acceptor carbons in the native enzyme and may enhance the role of tunneling in the hydride transfer reaction.

Cerebral protein synthesis in a genetic mouse model of phenylketonuria

Local rates of cerebral protein synthesis (lCPSleu) were measured with the quantitative autoradiographic [1-14C]leucine method in a genetic mouse model (Pahenu2) of phenylketonuria. As in the human disease, Pahenu2 mice have a mutation in the gene for phenylalanine hydroxylase. We compared adult homozygous (HMZ) and heterozygous (HTZ) Pahenu2 mice with the background strain (BTBR). Arterial plasma concentrations of phenylalanine (Phe) were elevated in both HMZ and HTZ mutants by 21 times and 38%, respectively. In the total acid-soluble pool in brain concentrations of Phe were higher and other neutral amino acids lower in HMZ mice compared with either HTZ or BTBR mice indicating a partial saturation of the l-amino acid carrier at the blood brain barrier by the elevated plasma Phe concentrations. In a series of steady-state experiments, the contribution of leucine from the arterial plasma to the tRNA-bound pool in brain was found to be statistically significantly reduced in HMZ mice compared with the other groups, indicating that a greater fraction of leucine in the precursor pool for protein synthesis is derived from protein degradation. We found reductions in lCPSleu of about 20% throughout the brain in the HMZ mice compared with the other two groups, but no reductions in brain concentrations of tRNA-bound neutral amino acids. Our results in the mouse model suggest that in untreated phenylketonuria in adults, the partial saturation of the l-amino acid transporter at the blood–brain barrier may not underlie a reduction in cerebral protein synthesis.