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.

Structure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

Partially Observed Markov Random Fields Are Variable Neighborhood Random Fields

The present paper has two goals. First to present a natural example of a new class of random fields which are the variable neighborhood random fields. The example we consider is a partially observed nearest neighbor binary Markov random field. The second goal is to establish sufficient conditions ensuring that the variable neighborhoods are almost surely finite. We discuss the relationship between the almost sure finiteness of the interaction neighborhoods and the presence/absence of phase transition of the underlying Markov random field. In the case where the underlying random field has no phase transition we show that the finiteness of neighborhoods depends on a specific relation between the noise level and the minimum values of the one-point specification of the Markov random field. The case in which there is phase transition is addressed in the frame of the ferromagnetic Ising model. We prove that the existence of infinite interaction neighborhoods depends on the phase.

Proteomic Analysis of Chloroplast-to-Chromoplast Transition in Tomato Reveals Metabolic Shifts Coupled with Disrupted Thylakoid Biogenesis Machinery and Elevated Energy-Production Components

A comparative proteomic approach was performed to identify differentially expressed proteins in plastids at three stages of tomato (Solanum lycopersicum) fruit ripening (mature-green, breaker, red). Stringent curation and processing of the data from three independent replicates identified 1,932 proteins among which 1,529 were quantified by spectral counting. The quantification procedures have been subsequently validated by immunoblot analysis of six proteins representative of distinct metabolic or regulatory pathways. Among the main features of the chloroplast-to-chromoplast transition revealed by the study, chromoplastogenesis appears to be associated with major metabolic shifts: (1) strong decrease in abundance of proteins of light reactions (photosynthesis, Calvin cycle, photorespiration) and carbohydrate metabolism (starch synthesis/degradation), mostly between breaker and red stages and (2) increase in terpenoid biosynthesis (including carotenoids) and stress-response proteins (ascorbate-glutathione cycle, abiotic stress, redox, heat shock). These metabolic shifts are preceded by the accumulation of plastid-encoded acetyl Coenzyme A carboxylase D proteins accounting for the generation of a storage matrix that will accumulate carotenoids. Of particular note is the high abundance of proteins involved in providing energy and in metabolites import. Structural differentiation of the chromoplast is characterized by a sharp and continuous decrease of thylakoid proteins whereas envelope and stroma proteins remain remarkably stable. This is coincident with the disruption of the machinery for thylakoids and photosystem biogenesis (vesicular trafficking, provision of material for thylakoid biosynthesis, photosystems assembly) and the loss of the plastid division machinery. Altogether, the data provide new insights on the chromoplast differentiation process while enriching our knowledge of the plant plastid proteome.

SINGULARLY PERTURBED DISCOUNTED MARKOV CONTROL PROCESSES IN A GENERAL STATE SPACE

This paper studies the asymptotic optimality of discrete-time Markov decision processes (MDPs) with general state space and action space and having weak and strong interactions. By using a similar approach as developed by Liu, Zhang, and Yin [Appl. Math. Optim., 44 (2001), pp. 105-129], the idea in this paper is to consider an MDP with general state and action spaces and to reduce the dimension of the state space by considering an averaged model. This formulation is often described by introducing a small parameter epsilon > 0 in the definition of the transition kernel, leading to a singularly perturbed Markov model with two time scales. Our objective is twofold. First it is shown that the value function of the control problem for the perturbed system converges to the value function of a limit averaged control problem as epsilon goes to zero. In the second part of the paper, it is proved that a feedback control policy for the original control problem defined by using an optimal feedback policy for the limit problem is asymptotically optimal. Our work extends existing results of the literature in the following two directions: the underlying MDP is defined on general state and action spaces and we do not impose strong conditions on the recurrence structure of the MDP such as Doeblin's condition.

Magnetic and optical investigation of 40SiO(2)center dot 30Na(2)O center dot 1Al(2)O(3)center dot(29-x) B2O3 center dot xFe(2)O(3) glass matrix

Samples of 40SiO(2)center dot 30Na(2)O center dot 1Al(2)O(3)center dot(29 - x)B2O3 center dot xFe(2)O(3) (mol%), with 0.0 <= x <= 17.5, were prepared by the fusion method and investigated by electron paramagnetic resonance (EPR), optical absorption (OA) and Mossbauer spectroscopy (MS). The EPR spectra of the as-synthesized samples exhibit two well-defined EPR signals around g = 4.27 and g = 2.01 and a visible EPR shoulder around g = 6.4, assigned to isolated Fe3+ ion complexes (g = 4.27 and g = 6.4) and Fe3+-based clusters (g = 2.01). Analyses of both EPR line intensity and line width support the model picture of Fe3+-based clusters built in from two sources of isolated ions, namely Fe2+ and Fe3+; the ferrous ion being used to build in iron-based clusters at lower x-content (below about x = 2.5%) whereas the ferric ion is used to build in iron-based clusters at higher x-content (above about x = 2.5%). The presence of Fe2+ ions incorporated within the glass template is supported by OA data with a strong band around 1100 nm due to the spin-allowed E-5(g)-T-5(2g) transition in an octahedral coordination with oxygen. Additionally, Mossbauer data (isomer shift and quadrupole splitting) confirm incorporation of both Fe2+ and Fe3+ ions within the template, more likely in tetrahedral-like environments. We hypothesize that ferrous ions are incorporated within the glass template as FeO4 complex resulting from replacing silicon in non-bridging oxygen (SiO3O-) sites whereas ferric ions are incorporated as FeO4 complex resulting from replacing silicon in bridging-like oxygen silicate groups (SiO4). (C) 2012 Elsevier Masson SAS. All rights reserved.

The Extracellular Matrix of the Lateral Pharyngeal Wall in Obstructive Sleep Apnea

Study Objectives: To compare the components of the extracellular matrix in the lateral pharyngeal muscular wall in patients with and without obstructive sleep apnea (OSA). This may help to explain the origin of the increased collapsibility of the pharynx in patients with OSA. Design: Specimens from the superior pharyngeal constrictor muscle, obtained during pharyngeal surgeries, were evaluated using histochemical and immunohistochemical analyses to determine the fractional area of collagen types I and II, elastic fibers, versican, fibronectin, and matrix metalloproteinases 1 and 2 in the endomysium. Setting: Academic tertiary center. Patiens: A total of 51 nonobese adult patients, divided into 38 patients with OSA and 13 nonsnoring control subjects without OSA. Interventions: Postintervention study performed on tissues from patients after elective surgery. Measurements and Results: Pharyngeal muscles of patients with OSA had significantly more collagen type I than pharyngeal muscles in control subjects. Collagen type I was correlated positively and independently with age. The other tested components of the extracellular matrix did not differ significantly between groups. In a logistic regression, an additive effect of both the increase of collagen type I and the increase in age with the presence of OSA was observed (odds ratio (OR), 2.06; 95% confidence interval (CI), 1.17-3.63), when compared with the effect of increased age alone (OR, 1.11; 95% CI, 1.03-1.20). Conclusion: Collagen type I in the superior pharyngeal constrictor muscle was more prevalent in patients with OSA and also increased with age. It was hypothesized that this increase could delay contractile-relaxant responses in the superior pharyngeal constrictor muscle at the expiratory-inspiratory phase transition, thus increasing pharyngeal collapsibility.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.