Prominent Effect of Soil Network Heterogeneity on Microbial Invasion

Using a network representation for real soil samples and mathematical models for microbial spread, we show that the structural heterogeneity of the soil habitat may have a very significant influence on the size of microbial invasions of the soil pore space. In particular, neglecting the soil structural heterogeneity may lead to a substantial underestimation of microbial invasion. Such effects are explained in terms of a crucial interplay between heterogeneity in microbial spread and heterogeneity in the topology of soil networks. The main influence of network topology on invasion is linked to the existence of long channels in soil networks that may act as bridges for transmission of microorganisms between distant parts of soil.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

Emergence of sensory selection mechanisms in Artificial Life simulations

Background The evolutionary advantages of selective attention are unclear. Since the study of selective attention began, it has been suggested that the nervous system only processes the most relevant stimuli because of its limited capacity [1]. An alternative proposal is that action planning requires the inhibition of irrelevant stimuli, which forces the nervous system to limit its processing [2]. An evolutionary approach might provide additional clues to clarify the role of selective attention. Methods We developed Artificial Life simulations wherein animals were repeatedly presented two objects, "left" and "right", each of which could be "food" or "non-food." The animals' neural networks (multilayer perceptrons) had two input nodes, one for each object, and two output nodes to determine if the animal ate each of the objects. The neural networks also had a variable number of hidden nodes, which determined whether or not it had enough capacity to process both stimuli (Table 1). The evolutionary relevance of the left and the right food objects could also vary depending on how much the animal's fitness was increased when ingesting them (Table 1). We compared sensory processing in animals with or without limited capacity, which evolved in simulations in which the objects had the same or different relevances. Table 1. Nine sets of simulations were performed, varying the values of food objects and the number of hidden nodes in the neural networks. The values of left and right food were swapped during the second half of the simulations. Non-food objects were always worth -3. The evolution of neural networks was simulated by a simple genetic algorithm. Fitness was a function of the number of food and non-food objects each animal ate and the chromosomes determined the node biases and synaptic weights. During each simulation, 10 populations of 20 individuals each evolved in parallel for 20,000 generations, then the relevance of food objects was swapped and the simulation was run again for another 20,000 generations. The neural networks were evaluated by their ability to identify the two objects correctly. The detectability (d') for the left and the right objects was calculated using Signal Detection Theory [3]. Results and conclusion When both stimuli were equally relevant, networks with two hidden nodes only processed one stimulus and ignored the other. With four or eight hidden nodes, they could correctly identify both stimuli. When the stimuli had different relevances, the d' for the most relevant stimulus was higher than the d' for the least relevant stimulus, even when the networks had four or eight hidden nodes. We conclude that selection mechanisms arose in our simulations depending not only on the size of the neuron networks but also on the stimuli's relevance for action.

Relationship between Vitamin D Receptor gene polymorphisms and the components of metabolic syndrome

Abstract Background The Vitamin D Receptor gene (VDR) is expressed in many tissues and modulates the expression of several other genes. The purpose of this study was to investigate the association between metabolic syndrome (MetSyn) with the presence of VDR 2228570 C > T and VDR 1544410 A > G polymorphisms in Brazilian adults. Methods Two hundred forty three (243) individuals were included in a cross-sectional study. MetSyn was classified using the criteria proposed by National Cholesterol Educational Program - Adult Treatment Panel III. Insulin resistance and β cell secretion were estimated by the mathematical models of HOMA IR and β, respectively. The VDR 2228570 C > T and VDR 1544410 A > G polymorphisms were detected by enzymatic digestion and confirmed by allele specific PCR or amplification of refractory mutation. Results Individuals with MetSyn and heterozygosis for VDR 2228570 C > T have higher concentrations of iPTH and HOMA β than those without this polymorphism, and subjects with recessive homozygosis for the same polymorphisms presented higher insulin resistance than those with the heterozygous genotype. There is no association among VDR 1544410 A > G and components of MetSyn, HOMA IR and β, serum vitamin D (25(OH)D3) and intact parathormone (iPTH) levels in patients with MetSyn. A significant lower concentration of 25(OH)D3 was observed only in individuals without MetSyn in the VDR 1544410 A > G genotype. Additionally, individuals without MetSyn and heterozygosis for VDR 2228570 C > T presented higher concentration of triglycerides and lower HDL than those without this polymorphism. Conclusions Using two common VDR polymorphism data suggests they may influence insulin secretion, insulin resistance an serum HDL-cholesterol in our highly heterogeneous population. Whether VDR polymorphism may influence the severity of MetSyn component disorder, warrants examination in larger cohorts used for genome-wide association studies.

Performance estimation for concretes made with recycled aggregates of construction and demolition waste of some Brazilian cities

The aim of this paper is to verify the influence of composition variability of recycled aggregates (RA) of construction and demolition wastes (CDW) on the performance of concretes. Performance was evaluated building mathematical models for compressive strength, modulus of elasticity and drying shrinkage. To obtain such models, an experimental program comprising 50 concrete mixtures was carried out. Specimens were casted, tested and results for compressive strength, modulus of elasticity and drying shrinkage were statistically analyzed. Models inputs are CDW composition observed at seven Brazilian cities. Results confirm that using RA from CDW for concrete building is quite feasible, independently of its composition, once compressive strength and modulus of elasticity still reached considerable values. We concluded the variability presented by recycled aggregates of CDW does not compromise their use for concrete building. However, this information must be used with caution, and experimental tests should always be performed to certify concrete properties.

Multimodality and flexibility of stochastic gene expression

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.

Computational analyses on the structure-function relation in ion channels

Ion channels are protein molecules, embedded in the lipid bilayer of the cell membranes. They act as powerful sensing elements switching chemicalphysical stimuli into ion-fluxes. At a glance, ion channels are water-filled pores, which can open and close in response to different stimuli (gating), and one once open select the permeating ion species (selectivity). They play a crucial role in several physiological functions, like nerve transmission, muscular contraction, and secretion. Besides, ion channels can be used in technological applications for different purpose (sensing of organic molecules, DNA sequencing). As a result, there is remarkable interest in understanding the molecular determinants of the channel functioning. Nowadays, both the functional and the structural characteristics of ion channels can be experimentally solved. The purpose of this thesis was to investigate the structure-function relation in ion channels, by computational techniques. Most of the analyses focused on the mechanisms of ion conduction, and the numerical methodologies to compute the channel conductance. The standard techniques for atomistic simulation of complex molecular systems (Molecular Dynamics) cannot be routinely used to calculate ion fluxes in membrane channels, because of the high computational resources needed. The main step forward of the PhD research activity was the development of a computational algorithm for the calculation of ion fluxes in protein channels. The algorithm - based on the electrodiffusion theory - is computational inexpensive, and was used for an extensive analysis on the molecular determinants of the channel conductance. The first record of ion-fluxes through a single protein channel dates back to 1976, and since then measuring the single channel conductance has become a standard experimental procedure. Chapter 1 introduces ion channels, and the experimental techniques used to measure the channel currents. The abundance of functional data (channel currents) does not match with an equal abundance of structural data. The bacterial potassium channel KcsA was the first selective ion channels to be experimentally solved (1998), and after KcsA the structures of four different potassium channels were revealed. These experimental data inspired a new era in ion channel modeling. Once the atomic structures of channels are known, it is possible to define mathematical models based on physical descriptions of the molecular systems. These physically based models can provide an atomic description of ion channel functioning, and predict the effect of structural changes. Chapter 2 introduces the computation methods used throughout the thesis to model ion channels functioning at the atomic level. In Chapter 3 and Chapter 4 the ion conduction through potassium channels is analyzed, by an approach based on the Poisson-Nernst-Planck electrodiffusion theory. In the electrodiffusion theory ion conduction is modeled by the drift-diffusion equations, thus describing the ion distributions by continuum functions. The numerical solver of the Poisson- Nernst-Planck equations was tested in the KcsA potassium channel (Chapter 3), and then used to analyze how the atomic structure of the intracellular vestibule of potassium channels affects the conductance (Chapter 4). As a major result, a correlation between the channel conductance and the potassium concentration in the intracellular vestibule emerged. The atomic structure of the channel modulates the potassium concentration in the vestibule, thus its conductance. This mechanism explains the phenotype of the BK potassium channels, a sub-family of potassium channels with high single channel conductance. The functional role of the intracellular vestibule is also the subject of Chapter 5, where the affinity of the potassium channels hEag1 (involved in tumour-cell proliferation) and hErg (important in the cardiac cycle) for several pharmaceutical drugs was compared. Both experimental measurements and molecular modeling were used in order to identify differences in the blocking mechanism of the two channels, which could be exploited in the synthesis of selective blockers. The experimental data pointed out the different role of residue mutations in the blockage of hEag1 and hErg, and the molecular modeling provided a possible explanation based on different binding sites in the intracellular vestibule. Modeling ion channels at the molecular levels relates the functioning of a channel to its atomic structure (Chapters 3-5), and can also be useful to predict the structure of ion channels (Chapter 6-7). In Chapter 6 the structure of the KcsA potassium channel depleted from potassium ions is analyzed by molecular dynamics simulations. Recently, a surprisingly high osmotic permeability of the KcsA channel was experimentally measured. All the available crystallographic structure of KcsA refers to a channel occupied by potassium ions. To conduct water molecules potassium ions must be expelled from KcsA. The structure of the potassium-depleted KcsA channel and the mechanism of water permeation are still unknown, and have been investigated by numerical simulations. Molecular dynamics of KcsA identified a possible atomic structure of the potassium-depleted KcsA channel, and a mechanism for water permeation. The depletion from potassium ions is an extreme situation for potassium channels, unlikely in physiological conditions. However, the simulation of such an extreme condition could help to identify the structural conformations, so the functional states, accessible to potassium ion channels. The last chapter of the thesis deals with the atomic structure of the !- Hemolysin channel. !-Hemolysin is the major determinant of the Staphylococcus Aureus toxicity, and is also the prototype channel for a possible usage in technological applications. The atomic structure of !- Hemolysin was revealed by X-Ray crystallography, but several experimental evidences suggest the presence of an alternative atomic structure. This alternative structure was predicted, combining experimental measurements of single channel currents and numerical simulations. This thesis is organized in two parts, in the first part an overview on ion channels and on the numerical methods adopted throughout the thesis is provided, while the second part describes the research projects tackled in the course of the PhD programme. The aim of the research activity was to relate the functional characteristics of ion channels to their atomic structure. In presenting the different research projects, the role of numerical simulations to analyze the structure-function relation in ion channels is highlighted.