The retinoic-like juvenile hormone controls the looping of left-right asymmetric organs in Drosophila

In vertebrate development, the establishment of left-right asymmetry is essential for sidedness and the directional looping of organs like the heart. Both the nodal pathway and retinoic acid play major and conserved regulatory roles in these processes. We carried out a novel screen in Drosophila to identify mutants that specifically affect the looping of left-right asymmetric organs. We report the isolation of spin, a novel mutant in which the looping of the genitalia and spermiduct are incomplete; under-rotation of the genitalia indicates that spin controls looping morphogenesis but not direction, thus uncoupling left-right asymmetry and looping morphogenesis. spin is a novel, rotation-specific allele of the fasciclin2 (Fas2) gene, which encodes a cell-adhesion protein involved in several aspects of neurogenesis. In spin mutants, the synapses connecting specific neurosecretory cells to the corpora allata are affected. The corpus allatum is part of the ring gland and is involved in the control of juvenile hormone titers during development. Our genetic and pharmacological results indicate that Fas2(spin) rotation defects are linked to an abnormal endocrine function and an elevated level of juvenile hormone. As juvenile hormone is an insect sesquiterpenoid related to retinoic acid, these results establish a new genetic model for studying organ looping and demonstrate an evolutionarily conserved role for terpenoids in this process.     

Mechanical properties of symmetric and asymmetric DNA A-tracts: implications for looping and nucleosome positioning

A-tracts are functionally important DNA sequences which induce helix bending and have peculiar structural properties. While A-tract structure has been qualitatively well characterized, their mechanical properties remain controversial. A-tracts appear structurally rigid and resist nucleosome formation, but seem flexible in DNA looping. In this work, we investigate mechanical properties of symmetric A_nT_n and asymmetric A_2n tracts for n = 3, 4, 5 using two types of coarse-grained models. The first model represents DNA as an ensemble of interacting rigid bases with non-local quadratic deformation energy, the second one treats DNA as an anisotropically bendable and twistable elastic rod. Parameters for both models are inferred from microsecond long, atomic-resolution molecular dynamics simulations. We find that asymmetric A-tracts are more rigid than the control G/C-rich sequence in localized distortions relevant for nucleosome formation, but are more flexible in global bending and twisting relevant for looping. The symmetric tracts, in contrast, are more rigid than asymmetric tracts and the control, both locally and globally. Our results can reconcile the contradictory stiffness data on A-tracts and suggest symmetric A-tracts to be more efficient in nucleosome exclusion than the asymmetric ones. This would open a new possibility of gene expression manipulation using A-tracts.     

Stability and pattern formation for competing populations with asymmetric nonlocal coupling

We consider a model of two competing species with asymmetric nonlocal coupling in a competition for resources. The nonlocal coupling is via convolution integrals and the asymmetry is via convolution kernel functions which are not even functions of their arguments. The nonlocality is due to species mobility, so that at any fixed point in space the competition for resources depends not just on the populations at that point but on a suitably weighted average of the populations. We introduce two parameters, δ  , describing the extent of the coupling, with δ=0$\delta =0$ corresponding to local coupling, and α  , describing the extent of the asymmetry, with α=0$\alpha =0$ corresponding to symmetric nonlocal interactions. We consider the case where the model admits a stable coexistence equilibrium solution. We perform a linear stability analysis and show that this solution can be destabilized by sufficient nonlocality, i.e., when δ increases beyond a critical value. We consider two specific kernel functions, (i) an asymmetric Gaussian and (ii) an asymmetric stepfunction. We compute the stability boundary as a function of α, and for δ beyond the stability boundary we determine unstable wavenumber bands. We compute nonlinear patterns for δ significantly beyond the stability boundary. Patterns consist of arrays of islands, regions of nonzero population, separated by either near-deadzones where the populations are small, but nonzero, or by deadzones where populations are exponentially small and essentially extinct. We find solutions consisting of propagating traveling waves of islands, solutions exhibiting colony formation, where a colony is formed just ahead of an island and eventually grows as the parent island decays, and modulated traveling waves, where competition between the two species allows propagation and inhibits colony formation. We explain colony formation and the modulated traveling waves as due to a positive feedback mechanism associated with small variations in the amplitude of the parent island.     

Stability in cyclic epidemic models

A general formulation for a family of cyclic epidemic models with density-dependent feedback mechanisms and removed classes is presented. A parameter, , related to the basic reproductive rate determines the asymptotic behaviour of solutions of the model. It is shown that if <1 the trivial solution is globally stable, and if >1 it is conditionally stable. The results are applied to a set of differential equations that has been used to model the life cycle of a parasite that has two hosts.     

Stability analysis of within-host parasite models with delays

We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the parasite is cleared, if R0>1 and if a sufficient condition is satisfied we conclude to the global asymptotic stability (GAS) of the endemic equilibrium. For some generic class of models this condition reduces to R0>1. These results make possible to revisit some parasitic models including intracellular delays and to study their global stability.     

Stability of the endemic equilibrium in epidemic models with subpopulations

For two models of infectious diseases, thresholds are identified, and it is proved that above the threshold there is a unique endemic equilibrium which is locally asymptotically stable. Both models are for diseases for which infection confers immunity, and both have the population divided into subpopulations. One model is a system of ordinary differential equations and includes immunization. The other is a system of integrodifferential equations and includes class-age infectivity.     

Stability in a class of cyclic epidemic models with delay

A detailed analysis of a general class of SIRS epidemic models is given. Sufficient conditions are derived which guarantee the global stability of the endemic equilibrium solution. Further conditions are found which ensure instability for the equilibrium. Finally, the dependence of the stability on the contact number and the ratio of the mean length of infection to the mean removed time is considered.     

Stability in Gilpin and Ayala's models of competition

Summary Simple and effective conditions for global stability in a class of models for m competing species are given. A numerical method is used to establish a large finite region of attraction for the feasible equilibrium in Gilpin and Ayala's model of two competing Drosophila populations.     

Stability and stabilization for models of chemostats with multiple limiting substrates

We study chemostat models in which multiple species compete for two or more limiting nutrients. First, we consider the case where the nutrient flow and species removal rates and input nutrient concentrations are all given as positive constants. In that case, we use Brouwer degree theory to give conditions guaranteeing that the models admit globally asymptotically stable componentwise positive equilibrium points, from all componentwise positive initial states. Then we use the results to develop stabilization theory for a class of controlled chemostats with two or more limiting nutrients. For cases where the dilution rate and input nutrient concentrations can be selected as controls, we prove that many different componentwise positive equilibria can be made globally asymptotically stable. This extends the existing control results for chemostats with one limiting nutrient. We demonstrate our methods in simulations.     

Stability and stabilization for models of chemostats with multiple limiting substrates

We study chemostat models in which multiple species compete for two or more limiting nutrients. First, we consider the case where the nutrient flow and species removal rates and input nutrient concentrations are all given as positive constants. In that case, we use Brouwer degree theory to give conditions guaranteeing that the models admit globally asymptotically stable componentwise positive equilibrium points, from all componentwise positive initial states. Then we use the results to develop stabilization theory for a class of controlled chemostats with two or more limiting nutrients. For cases where the dilution rate and input nutrient concentrations can be selected as controls, we prove that many different componentwise positive equilibria can be made globally asymptotically stable. This extends the existing control results for chemostats with one limiting nutrient. We demonstrate our methods in simulations.     

Features selection and architecture optimization in connectionist systems

In this paper, we propose a features selection measure and an architecture optimization procedure for Multi-Layer Perceptrons (MLP). The algorithm presented in this contribution employs a heuristic measure named HVS (Heuristic for Variable Selection). This new measure allows us to identify and select important variables in the features space. This can be achieved by eliminating redundant features and those which do not contain enough relevant information. The proposed measure is used in a new procedure aimed at selecting the "best" MLP architecture given an initial structure. Application results for two generic problems: regression and discrimination, demonstrates the proposed selection algorithm's effectiveness in identifying optimized connectionist models with higher accuracy. Finally, an extension of HVS, named epsilonHVS, is proposed for discriminative features detection and architecture optimization for Time Delay Neural Networks models (TDNN).     

Stability of discrete one-dimensional population models

We give conditions for local and global stability of discrete one-dimensional population models. We give a new test for local stability when the derivative is −1. We give several sufficient conditions for global stability. We use these conditions to show that local and global stability coincide for the usual models from the literature and even for slightly more complicated models. We give population models, which are in some sense the simplest models, for which local and global stability do not coincide.     

Stability results for delayed-recruitment models in population dynamics

This paper relates the stability properties of a class of delay-difference equations to those of an associated scalar difference equation. Simple but powerful conditions for testing global stability are presented which are independent of the length of the time delay involved. For models which do not have globally stable equilibria, estimates of stability regions are obtained. Some well known baleen whale models are used to illustrate the results.     

Stability of differential susceptibility and infectivity epidemic models

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio R₀ ￡ 1{\mathcal{R}_0 \leq 1} and the existence and uniqueness of an endemic equilibrium when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when ${\mathcal{R}_0 >1 }${\mathcal{R}_0 >1 } . Our results encompass and generalize those of Hyman and Li (J Math Biol 50:626–644, 2005; Math Biosci Eng 3:89–100, 2006).     

Stability and asymmetric replication of the Bacillus subtilis 168 chromosome structure.

Chromosomal DNAs from a number of strains derived from Bacillus subtilis 168 were digested with restriction endonucleases NotI or SfiI, and the locations of chromosomal alterations were compared with the recently constructed standard NotI-SfiI restriction map (M. Itaya and T. Tanaka, J. Mol. Biol. 220:631-648, 1991). In general, the chromosome structure of B. subtilis 168 was found to be stable, as expected from the genetic stability of this species. DNA alterations, typically deletions, are formed in three limited loci on the chromosome. One of these alterations was characterized as a spontaneous deletion formed between rrn operons, and another occurred as a result of prophage SP beta excision. I found that oriC and terC are not located on precisely opposite sides of the chromosome. Replication in the counter clockwise direction was 196 kb longer than replication in the clockwise direction. The characteristic of length difference is not changed by deletion formation.     

Entropy loss in long-distance DNA looping

The entropy loss due to the formation of one or multiple loops in circular and linear DNA chains is calculated from a scaling approach in the limit of long chain segments. The analytical results allow us to obtain a fast estimate for the entropy loss for a given configuration. Numerical values obtained for some examples suggest that the entropy loss encountered in loop closure in typical genetic switches may become a relevant factor in comparison to both k(B)T and typical bond energies in biopolymers, which has to be overcome by the released bond energy between the looping contact sites.