Ana Paula S. Dias

Ibuprofen reverts antifungal resistance on Candida albicans showing overexpression of CDR genes

Several mechanisms may be associated with Candida albicans resistance to azoles. Ibuprofen was described as being able to revert resistance related to efflux activity in Candida. The aim of this study was to uncover the molecular base of antifungal resistance in C. albicans clinical strains that could be reverted by ibuprofen. Sixty-two clinical isolates and five control strains of C. albicans were studied: the azole susceptibility phenotype was determined according to the Clinical Laboratory for Standards Institute, M27-A2 protocol and minimal inhibitory concentration values were recalculated with ibuprofen (100 microg mL(-1)); synergistic studies between fluconazole and FK506, a Cdr1p inhibitor, were performed using an agar disk diffusion assay and were compared with ibuprofen results. Gene expression was quantified by real-time PCR, with and without ibuprofen, regarding CDR1, CDR2, MDR1, encoding for efflux pumps, and ERG11, encoding for azole target protein. A correlation between susceptibility phenotype and resistance gene expression profiles was determined. Ibuprofen and FK506 showed a clear synergistic effect when combined with fluconazole. Resistant isolates reverting to susceptible after incubation with ibuprofen showed CDR1 and CDR2 overexpression especially of the latter. Conversely, strains that did not revert displayed a remarkable increase in ERG11 expression along with CDR genes. Ibuprofen did not alter resistance gene expression significantly (P>0.05), probably acting as a Cdrp blocker.

Linear equivalence and ODE-equivalence for coupled cell networks

Coupled cell systems are systems of ODEs, dened by ‘admissible’ vector elds, associated with a network whose nodes represent variables and whose edges specify couplings between nodes. It is known that non-isomorphic networks can correspond to the same space of admissible vector elds. Such networks are said to be ‘ODE-equivalent’. We prove that two networks are ODE-equivalent if and only if they determine the same space of linear vector elds; moreover, the variable associated with each node may be assumed 1-dimensional for that purpose. We briey discuss the combinatorics of the resulting linear algebra problem. AMS classication scheme numbers: 37C10 20L05

Patterns of synchrony in lattice dynamical systems

From the point of view of coupled systems developed by Stewart, Golubitsky and Pivato, lattice differential equations consist of choosing a phase space Rk for each point in a lattice, and a system of differential equations on each of these spaces Rk such that the whole system is translation invariant. The architecture of a lattice differential equation specifies the sites that are coupled to each other (nearest neighbour coupling (NN) is a standard example). A polydiagonal is a finite-dimensional subspace of phase space obtained by setting coordinates in different phase spaces as equal. There is a colouring of the network associated with each polydiagonal obtained by colouring any two cells that have equal coordinates with the same colour. A pattern of synchrony is a colouring associated with a polydiagonal that is flow-invariant for every lattice differential equation with a given architecture. We prove that every pattern of synchrony for a fixed architecture in planar lattice differential equations is spatially doubly-periodic, assuming that the couplings are sufficiently extensive. For example, nearest and next nearest neighbour couplings are needed for square and hexagonal couplings, but a third level of coupling is needed for the corresponding result to hold in rhombic and primitive cubic lattices. On planar lattices this result is known to fail if the network architecture consists only of NN. The techniques we develop to prove spatial periodicity and finiteness can be applied to other lattices as well.

Symmetry groupoids and admissible vector fields for coupled cell networks

The space of admissible vector fields, consistent with the structure of a network of coupled dynamical systems, can be specified in terms of the networks symmetry groupoid. The symmetry groupoid also determines the robust patterns of synchrony in the network – those that arise because of the network topology. In particular, synchronous cells can be identified in a canonical manner to yield a quotient network. Admissible vector fields on the original network induce admissible vector fields on the quotient, and any dynamical state of such an induced vector field can be lifted to the original network, yielding an analogous state in which certain sets of cells are synchronized. In the paper, necessary and sufficient conditions are specified for all admissible vector fields on the quotient to lift in this manner. These conditions are combinatorial in nature, and the proof uses invariant theory for the symmetric group. Also the symmetry groupoid of a quotient is related to that of the original network, and it is shown that there is a close analogy with the usual normalizer symmetry that arises in group-equivariant dynamics.

The Lattice of Synchrony Subspaces of a Coupled Cell Network: Characterization and Computation Algorithm

Coupled cell systems are networks of dynamical systems (the cells), where the links between the cells are described through the network structure, the coupled cell network. Synchrony subspaces are spaces defined in terms of equalities of certain cell coordinates that are flow-invariant for all coupled cell systems associated with a given network structure. The intersection of synchrony subspaces of a network is also a synchrony subspace of the network. It follows, then, that, given a coupled cell network, its set of synchrony subspaces, taking the inclusion partial order relation, forms a lattice. In this paper we show how to obtain the lattice of synchrony subspaces for a general network and present an algorithm that generates that lattice. We prove that this problem is reduced to obtain the lattice of synchrony subspaces for regular networks. For a regular network we obtain the lattice of synchrony subspaces based on the eigenvalue structure of the network adjacency matrix.

Hopf bifurcation with SN-symmetry

We study Hopf bifurcation with SN-symmetry for the standard absolutely irreducible action of SN obtained from the action of SN by permutation of N coordinates. Stewart (1996 Symmetry methods in collisionless many-body problems, J. Nonlinear Sci. 6 543–63) obtains a classification theorem for the C-axial subgroups of SN × S1. We use this classification to prove the existence of branches of periodic solutions with C-axial symmetry in systems of ordinary differential equations with SN-symmetry posed on a direct sum of two such SN-absolutely irreducible representations, as a result of a Hopf bifurcation occurring as a real parameter is varied. We determine the (generic) conditions on the coefficients of the fifth order SN × S1-equivariant vector field that describe the stability and criticality of those solution branches. We finish this paper with an application to the cases N = 4 and N = 5.

Invariants, equivariants and characters in symmetric bifurcation theory

In the analysis of stability in bifurcation problems it is often assumed that the (appropriate reduced) equations are in normal form. In the presence of symmetry, the truncated normal form is an equivariant polynomial map. Therefore, the determination of invariants and equivariants of the group of symmetries of the problem is an important step. In general, these are hard problems of invariant theory and, in most cases, they are tractable only through symbolic computer programs. Nevertheless, it is desirable to obtain some of the information about invariants and equivariants without actually computing them, for example, the number of linearly independent homogeneous invariants or equivariants of a certain degree. Generating functions for these dimensions are generally known as ‘Molien functions’. We obtain formulae for the number of linearly independent homogeneous invariants or equivariants for Hopf bifurcation in terms of characters. We also show how to construct Molien functions for invariants and equivariants for Hopf bifurcation. Our results are then applied to the computation of the number of invariants and equivariants for Hopf bifurcation for several finite groups and the continuous group O(3).

Minimal coupled cell networks

It is known that non-isomorphic coupled cell networks can have equivalent dynamics. Such networks are said to be ODE-equivalent and are related by a linear algebra condition involving their graph adjacency matrices. A network in an ODE-equivalence class is said to be minimal if it has a minimum number of edges. When studying a given network in an ODE-class it can be of great value to study instead a minimal network in that class. Here we characterize the minimal networks of an ODE-equivalence class—the canonical normal forms of the ODE-class. Moreover, we present an algorithm that computes the canonical normal forms for a given ODE-class. This goes through the calculation of vectors with minimum length contained in a cone of a lattice described in terms of the adjacency matrices of any network in the ODE-class.

Hilbert series for equivariant mappings restricted to invariant hyperplanes

Abstract In symmetric bifurcation theory it is often necessary to describe the restrictions of equivariant mappings to the fixed-point space of a subgroup. Such restrictions are equivariant under the normalizer of the subgroup, but this condition need not be the only constraint. We develop an approach to such questions in terms of Hilbert series – generating functions for the dimension of the space of equivariants of a given degree. We derive a formula for the Hilbert series of the restricted equivariants in the case when the subgroup is generated by a reflection, so the fixed-point space is a hyperplane. By comparing this Hilbert series with that of the normalizer, we can detect the occurrence of further constraints. The method is illustrated for the dihedral and symmetric groups.

Spatially Periodic Patterns of Synchrony in Lattice Networks

We consider n-dimensional Euclidean lattice networks with nearest neighbor coupling architecture. The associated lattice dynamical systems are infinite systems of ordinary differential equations, the cells, indexed by the points in the lattice. A pattern of synchrony is a finite-dimensional flow-invariant subspace for all lattice dynamical systems with the given network architecture. These subspaces correspond to a classification of the cells into k classes, or colors, and are described by a local coloring rule, named balanced coloring. Previous results with planar lattices show that patterns of synchrony can exhibit several behaviors such as periodicity. Considering sufficiently extensive couplings, spatial periodicity appears for all the balanced colorings with k colors. However, there is not a direct way of relating the local coloring rule and the coloring of the whole lattice network. Given an n-dimensional lattice network with nearest neighbor coupling architecture, and a local coloring rule with k c...