Solving inverse problems for biological models using the collage method for differential equations

In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.     

When size does matter: organelle size influences the properties of transport mediated by molecular motors

Background

Organelle transport is driven by the action of molecular motors. In this work, we studied the dynamics of organelles of different sizes with the aim of understanding the complex relation between organelle motion and microenvironment.

Methods

We used single particle tracking to obtain trajectories of melanosomes (pigmented organelles in Xenopus laevis melanophores). In response to certain hormones, melanosomes disperse in the cytoplasm or aggregate in the perinuclear region by the combined action of microtubule and actin motors.

Results and conclusions

Melanosome trajectories followed an anomalous diffusion model in which the anomalous diffusion exponent (α) provided information regarding the trajectories' topography and thus of the processes causing it. During aggregation, the directionality of big organelles was higher than that of small organelles and did not depend on the presence of either actin or intermediate filaments (IF). Depolymerization of IF significantly reduced α values of small organelles during aggregation but slightly affect their directionality during dispersion.

General significance

Our results could be interpreted considering that the number of copies of active motors increases with organelle size. Transport of big organelles was not influenced by actin or IF during aggregation showing that these organelles are moved processively by the collective action of dynein motors. Also, we found that intermediate filaments enhance the directionality of small organelles suggesting that this network keeps organelles close to the tracks allowing their efficient reattachment. The higher directionality of small organelles during dispersion could be explained considering the better performance of kinesin-2 vs. dynein at the single molecule level.     

Thermal ecology of two sympatric saxicolous lizards of the genus Phymaturus from the Payunia region (Argentina)

We evaluated the thermal biology of two sympatric saxicolous species of the genus Phymaturus, endemic from the Argentine Payunia region. Taking into account that the distributional range of Phymaturus roigorum (the largest species) is greater than the range of P. payuniae, we evaluated the habitat (type of rocks) used by these species. We recorded body temperature and operative temperatures in different habitats, and we determined the preferred body temperature in the laboratory. We compared the thermal quality of habitats occupied and not occupied by Phymaturus payuniae, and the accuracy and effectiveness of thermoregulation between species.     

Application of nonspecific commercial AMF inocula results in poor mycorrhization in Camellia japonica L.

Camellia japonica L. (Theaceae, Theales) is an acidophilic evergreen flowering shrub and is traded worldwide. Symbiotic associations between the roots of this plant species and arbuscular mycorrhizal fungi (AMF), commonly recognized as natural biofertilizers and biocontrol agents, have been poorly studied so far. The aim of our study was to verify whether the application of nonspecific commercial AMF-based inocula could succeed and improve the growth of C. japonica. An experiment was conducted concerning the application of commercial inocula constituted by a specific AMF isolate (Funneliformis mosseae) or a consortium of different fungi and bacteria as alternatives to fertilization in pot cultivated C. japonica ‘Dr. Burnside’. Several growth parameters, plant nutrition and mycorrhization levels were monitored at the end of plant cultivation. Generally, increases in some macroelements (Ca, Mg, K) and microelements (Cu, Mn, Fe, Zn) were detected in the root system of inoculated camellias, while only Cu and Mn accumulation was increased in the leaves. Plants inoculated with the consortium inoculum exhibited increased chlorophyll content and foliage diameter while plants inoculated with F. mosseae exhibited increased number of flowers. Based on the polymorphism of an 18S rDNA region, we assessed the inoculated AMF that colonized C. japonica roots. The experiments showed that the applied AMF poorly colonized the root system of C. japonica. We suggest that commercial AMF formulations should be more targeted and host-specific in order to successfully colonize the host root and, potentially, fully express their benefits.     

A Novel EPS-Producing Strain of Bacillus licheniformis Isolated from a Shallow Vent Off Panarea Island (Italy)

A haloalkaliphilic, thermophilic Bacillus strain (T14), isolated from a shallow hydrothermal vent of Panarea Island (Italy), produced a new exopolysaccharide (EPS). Phylogenetic analysis based on 16S rRNA gene sequences showed that strain T14 was highly related (99 % similarity) to Bacillus licheniformis DSM 13^T and Bacillus sonorensis DSM 13779^T. Further DNA–DNA hybridization analysis revealed 79.40 % similarity with B. licheniformis DSM 13^T and 39.12 % with B. sonorensis DSM 13779^T. Sucrose (5 %) was the most efficient carbon source for growth and EPS production. The highest EPS production (366 mg l^?1) was yielded in fermenter culture at 300 rpm after 48 h of incubation. The purified fraction EPS1 contained fructose/fucose/glucose/galactosamine/mannose in a relative proportion of 1.0:0.75:0.28:tr:tr and possessed a molecular weight of 1,000 kDa displaying a trisaccharide unit constituted by sugars with a β-manno-pyranosidic configuration. Screening for biological activity showed anti-cytotoxic effect of EPS1 against Avarol in brine shrimp test, indicating a potential use in the development of novel drugs.     

Anxiolytic Properties of New Chemical Entity, 5TIO1

2-[(2,6-dichlorobenzylidene)amino]-5,6-dihydro-4H-cyclopenta[b]thiophene-3-carbonitrile), 5TIO1, is a new 2-aminothiophene derivative with a promising pharmacological activity. The aim of this work was to evaluate the potential anxiolytic effect of 5TIO1 in animal models. In the elevated plus-maze test, 5TIO1 (0.1, 1.0 and 10.0 mg/kg, i.p) increased the time of permanence and the number of entries in the open arms. In the light/dark box test, 5TIO1 at dose of 0.1 mg/kg (i.p) also showed anxiolytic-like effect indicated by an increase in the time spent in the light box, similar to diazepam 2.0 mg/kg (i.p). 5TIO1 groups did not change locomotor and coordination activities in open field and rotarod tests, respectively, when compared to vehicle. Dose dependent process was not observed and the anxiolytic effects demonstrated were not completely reversed by flumazenil 25 mg/kg (i.p). Our results suggest that 5TIO1 can bind with other receptors, besides the benzodiazepine site of the GABA receptor in mouse brain.