Nonequilibrium effects in DNA microarrays: a multiplatform study

It has recently been shown that in some DNA microarrays the time needed to reach thermal equilibrium may largely exceed the typical experimental time, which is about 15h in standard protocols (Hooyberghs et al. Phys. Rev. E 81, 012901 (2010)). In this paper we discuss how this breakdown of thermodynamic equilibrium could be detected in microarray experiments without resorting to real time hybridization data, which are difficult to implement in standard experimental conditions. The method is based on the analysis of the distribution of fluorescence intensities I from different spots for probes carrying base mismatches. In thermal equilibrium and at sufficiently low concentrations, log I is expected to be linearly related to the hybridization free energy $\Delta G$ with a slope equal to $1/RT_{exp}$, where $T_{exp}$ is the experimental temperature and R is the gas constant. The breakdown of equilibrium results in the deviation from this law. A model for hybridization kinetics explaining the observed experimental behavior is discussed, the so-called 3-state model. It predicts that deviations from equilibrium yield a proportionality of $\log I$ to $\Delta G/RT_{eff}$. Here, $T_{eff}$ is an effective temperature, higher than the experimental one. This behavior is indeed observed in some experiments on Agilent arrays. We analyze experimental data from two other microarray platforms and discuss, on the basis of the results, the attainment of equilibrium in these cases. Interestingly, the same 3-state model predicts a (dynamical) saturation of the signal at values below the expected one at equilibrium.Comment: 27 pages, 9 figures, 1 tabl

Dynamics-dependent criticality in models with q absorbing states

We study a one-dimensional, nonequilibrium Potts-like model which has $q$ symmetric absorbing states. For $q=2$, as expected, the model belongs to the parity conserving universality class. For $q=3$ the critical behaviour depends on the dynamics of the model. Under a certain dynamics it remains generically in the active phase, which is also the feature of some other models with three absorbing states. However, a modified dynamics induces a parity conserving phase transition. Relations with branching-annihilating random walk models are discussed in order to explain such a behaviour.Comment: 5 pages, 5 eps figures included, Phys.Rev.E (accepted

Absorbing state phase transitions with quenched disorder

Quenched disorder - in the sense of the Harris criterion - is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.Comment: 17 pages, 8 figure

The generalized contact process with n absorbing states

We investigate the critical properties of a one dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with $n \leq 4$ by means of the non-hermitian density matrix renormalization group. For n=1 and n=2 we find that the model is respectively in the directed percolation and parity conserving universality class, consistent with previous studies. For n=3 and n=4, the model is in the active phase in the whole parameter space and the critical point is shifted to the limit of one infinite reaction rate. We show that in this limit the dynamics of the model can be mapped onto that of a zero temperature n-state Potts model. On the basis of our numerical and analytical results we conjecture that the model is in the same universality class for all $n \geq 3$ with exponents $z = \nu_\|/\nu_\perp = 2$, $\nu_\perp = 1$ and $\beta = 1$. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For n=3 we also show that, upon breaking the symmetry to a lower one ($Z_2$), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters.Comment: 10 pages, RevTeX, and 10 PostScript figures include

Phase transitions in nonequilibrium d-dimensional models with q absorbing states

A nonequilibrium Potts-like model with $q$ absorbing states is studied using Monte Carlo simulations. In two dimensions and $q=3$ the model exhibits a discontinuous transition. For the three-dimensional case and $q=2$ the model exhibits a continuous, transition with $\beta=1$ (mean-field). Simulations are inconclusive, however, in the two-dimensional case for $q=2$. We suggest that in this case the model is close to or at the crossing point of lines separating three different types of phase transitions. The proposed phase diagram in the $(q,d)$ plane is very similar to that of the equilibrium Potts model. In addition, our simulations confirm field-theory prediction that in two dimensions a branching-annihilating random walk model without parity conservation belongs to the directed percolation universality class.Comment: 8 pages, figures included, accepted in Phys.Rev.

The one-dimensional contact process: duality and renormalisation

We study the one-dimensional contact process in its quantum version using a recently proposed real space renormalisation technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates which are comparable in accuracy with the best known in the literature.Comment: 15 page

Strong disorder fixed point in absorbing state phase transitions

The effect of quenched disorder on non-equilibrium phase transitions in the directed percolation universality class is studied by a strong disorder renormalization group approach and by density matrix renormalization group calculations. We show that for sufficiently strong disorder the critical behaviour is controlled by a strong disorder fixed point and in one dimension the critical exponents are conjectured to be exact: \beta=(3-\sqrt{5})/2 and \nu_\perp=2. For disorder strengths outside the attractive region of this fixed point, disorder dependent critical exponents are detected. Existing numerical results in two dimensions can be interpreted within a similar scenario.Comment: final version as accepted for PRL, contains new results in two dimension

Low-density series expansions for directed percolation IV. Temporal disorder

We introduce a model for temporally disordered directed percolation in which the probability of spreading from a vertex $(t,x)$, where $t$ is the time and $x$ is the spatial coordinate, is independent of $x$ but depends on $t$. Using a very efficient algorithm we calculate low-density series for bond percolation on the directed square lattice. Analysis of the series yields estimates for the critical point $p_c$ and various critical exponents which are consistent with a continuous change of the critical parameters as the strength of the disorder is increased.Comment: 11 pages, 3 figure

One-dimensional Nonequilibrium Kinetic Ising Models with local spin-symmetry breaking: N-component branching annihilation transition at zero branching rate

The effects of locally broken spin symmetry are investigated in one dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster mean field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed for the first time.Comment: 6 pages, 5 figures included, 2 new tables added, to appear in PR