Minimum entropy production principle from a dynamical fluctuation law

The minimum entropy production principle provides an approximative variational characterization of close-to-equilibrium stationary states, both for macroscopic systems and for stochastic models. Analyzing the fluctuations of the empirical distribution of occupation times for a class of Markov processes, we identify the entropy production as the large deviation rate function, up to leading order when expanding around a detailed balance dynamics. In that way, the minimum entropy production principle is recognized as a consequence of the structure of dynamical fluctuations, and its approximate character gets an explanation. We also discuss the subtlety emerging when applying the principle to systems whose degrees of freedom change sign under kinematical time-reversal.Comment: 17 page

Survival probability of a particle in a sea of mobile traps: A tale of tails

We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement of each trap grows as $t^{\gamma}$ with $0\leq \gamma \leq 1$. Starting from a continuous time random walk (CTRW) description of the motion of the particle and of the traps, we derive lower and upper bounds for $P(t)$ and show that for $\gamma \leq 2/(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $\gamma > 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $\gamma$ regime no longer coincide and the decay law for the survival probability of the $A$ particle remains ambiguous

Tunneling and Metastability of continuous time Markov chains

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states

Quantum state estimation and large deviations

In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends previous results concerning the estimation of the spectrum of \rho. We show that it is consistent (i.e. the original input state \rho is recovered with certainty if N \to \infty), analyze its large deviation behavior, and calculate explicitly the corresponding rate function which describes the exponential decrease of error probabilities in the limit N \to \infty. Finally we discuss the question whether the proposed scheme provides the fastest possible decay of error probabilities.Comment: LaTex2e, 40 pages, 2 figures. Substantial changes in Section 4: one new subsection (4.1) and another (4.2 was 4.1 in the previous version) completely rewritten. Minor changes in Sect. 2 and 3. Typos corrected. References added. Accepted for publication in Rev. Math. Phy

Regulation of ABCA1 by AMD-Associated Genetic Variants and Hypoxia in iPSC-RPE

Age-related macular degeneration (AMD) is a progressive disease of the macula characterized by atrophy of the retinal pigment epithelium (RPE) and photoreceptor degeneration, leading to severe vision loss at advanced stages in the elderly population. Impaired reverse cholesterol transport (RCT) as well as intracellular lipid accumulation in the RPE are implicated in AMD pathogenesis. Here, we focus on ATP-binding cassette transporter A1 (ABCA1), a major cholesterol transport protein in the RPE, and analyze conditions that lead to ABCA1 dysregulation in induced pluripotent stem cell (iPSC)-derived RPE cells (iRPEs). Our results indicate that the risk-conferring alleles rs1883025 (C) and rs2740488 (A) in ABCA1 are associated with increased ABCA1 mRNA and protein levels and reduced efficiency of cholesterol efflux from the RPE. Hypoxia, an environmental risk factor for AMD, reduced expression of ABCA1 and increased intracellular lipid accumulation. Treatment with a liver X receptor (LXR) agonist led to an increase in ABCA1 expression and reduced lipid accumulation. Our data strengthen the homeostatic role of cholesterol efflux in the RPE and suggest that increasing cellular cholesterol export by stimulating ABCA1 expression might lessen lipid load, improving RPE survival and reducing the risk of developing AMD

The target problem with evanescent subdiffusive traps

We calculate the survival probability of a stationary target in one dimension surrounded by diffusive or subdiffusive traps of time-dependent density. The survival probability of a target in the presence of traps of constant density is known to go to zero as a stretched exponential whose specific power is determined by the exponent that characterizes the motion of the traps. A density of traps that grows in time always leads to an asymptotically vanishing survival probability. Trap evanescence leads to a survival probability of the target that may be go to zero or to a finite value indicating a probability of eternal survival, depending on the way in which the traps disappear with time

Heat flow in chains driven by thermal noise

We consider the large deviation function for a classical harmonic chain composed of N particles driven at the end points by heat reservoirs, first derived in the quantum regime by Saito and Dhar and in the classical regime by Saito and Dhar and Kundu et al. Within a Langevin description we perform this calculation on the basis of a standard path integral calculation in Fourier space. The cumulant generating function yielding the large deviation function is given in terms of a transmission Green's function and is consistent with the fluctuation theorem. We find a simple expression for the tails of the heat distribution which turn out to decay exponentially. We, moreover, consider an extension of a single particle model suggested by Derrida and Brunet and discuss the two-particle case. We also discuss the limit for large N and present a closed expression for the cumulant generating function. Finally, we present a derivation of the fluctuation theorem on the basis of a Fokker-Planck description. This result is not restricted to the harmonic case but is valid for a general interaction potential between the particles.Comment: Latex: 26 pages and 9 figures, appeared in J. Stat. Mech. P04005 (2012

Detection of Variants in 15 Genes in 87 Unrelated Chinese Patients with Leber Congenital Amaurosis

BACKGROUND: Leber congenital amaurosis (LCA) is the earliest onset and most severe form of hereditary retinal dystrophy. So far, full spectrum of variations in the 15 genes known to cause LCA has not been systemically evaluated in East Asians. Therefore, we performed comprehensive detection of variants in these 15 genes in 87 unrelated Han Chinese patients with LCA. METHODOLOGY/PRINCIPAL FINDINGS: The 51 most frequently mutated exons and introns in the 15 genes were selected for an initial scan using cycle sequencing. All the remaining exons in 11 of the 15 genes were subsequently sequenced. Fifty-three different variants were identified in 44 of the 87 patients (50.6%), involving 78 of the 88 alleles (11 homozygous and 56 heterozygous variants). Of the 53 variants, 35 (66%) were novel pathogenic mutations. In these Chinese patients, variants in GUCY2D are the most common cause of LCA (16.1% cases), followed by CRB1 (11.5%), RPGRIP1 (8%), RPE65 (5.7%), SPATA7 (4.6%), CEP290 (4.6%), CRX (3.4%), LCA5 (2.3%), MERTK (2.3%), AIPL1 (1.1%), and RDH12 (1.1%). This differs from the variation spectrum described in other populations. An initial scan of 55 of 215 PCR amplicons, including 214 exons and 1 intron, detected 83.3% (65/78) of the mutant alleles ultimately found in these 87 patients. In addition, sequencing only 9 exons would detect over 50% of the identified variants and require less than 5% of the labor and cost of comprehensive sequencing for all exons. CONCLUSIONS/SIGNIFICANCE: Our results suggest that specific difference in the variation spectrum found in LCA patients from the Han Chinese and other populations are related by ethnicity. Sequencing exons in order of decreasing risk is a cost-effective way to identify causative mutations responsible for LCA, especially in the context of genetic counseling for individual patients in a clinical setting

Multiple domains in the Crumbs Homolog 2a (Crb2a) protein are required for regulating rod photoreceptor size

Background Vertebrate retinal photoreceptors are morphologically complex cells that have two apical regions, the inner segment and the outer segment. The outer segment is a modified cilium and is continuously regenerated throughout life. The molecular and cellular mechanisms that underlie vertebrate photoreceptor morphogenesis and the maintenance of the outer segment are largely unknown. The Crumbs (Crb) complex is a key regulator of apical membrane identity and size in epithelia and in Drosophila photoreceptors. Mutations in the human gene CRUMBS HOMOLOG 1 (CRB1) are associated with early and severe vision loss. Drosophila Crumbs and vertebrate Crb1 and Crumbs homolog 2 (Crb2) proteins are structurally similar, all are single pass transmembrane proteins with a large extracellular domain containing multiple laminin- and EGF-like repeats and a small intracellular domain containing a FERM-binding domain and a PDZ-binding domain. In order to begin to understand the role of the Crb family of proteins in vertebrate photoreceptors we generated stable transgenic zebrafish in which rod photoreceptors overexpress full-length Crb2a protein and several other Crb2a constructs engineered to lack specific domains. Results We examined the localization of Crb2a constructs and their effects on rod morphology. We found that only the full-length Crb2a protein approximated the normal localization of Crb2a protein apical to adherens junctions in the photoreceptor inner segment. Several Crb2a construct proteins localized abnormally to the outer segment and one construct localized abnormally to the cell body. Overexpression of full-length Crb2a greatly increased inner segment size while expression of several other constructs increased outer segment size. Conclusions Our observations suggest that particular domains in Crb2a regulate its localization and thus may regulate its regionalized function. Our results also suggest that the PDZ-binding domain in Crb2a might bring a protein(s) into the Crb complex that alters the function of the FERM-binding domain

Disruption of the basal body protein POC1B results in autosomal-recessive cone-rod dystrophy

Exome sequencing revealed a homozygous missense mutation (c.317C>G [p.Arg106Pro]) in POC1B, encoding POC1 centriolar protein B, in three siblings with autosomal-recessive cone dystrophy or cone-rod dystrophy and compound-heterozygous POC1B mutations (c.199_201del [p.G1n67del] and c.810+1G>T) in an unrelated person with cone-rod dystrophy. Upon overexpression of POC1B in human TERT-immortalized retinal pigment epithelium 1 cells, the encoded wild-type protein localized to the basal body of the primary cilium, whereas this localization was lost for p.Arg106Pro and p.G1n67del variant forms of POC1B. Morpholino-oligonucleotide-induced knockdown of poc1b translation in zebrafish resulted in a dose-dependent small-eye phenotype, impaired optokinetic responses, and decreased length of photoreceptor outer segments. These ocular phenotypes could partially be rescued by wild-type human POC1B mRNA, but not by c.199_201del and c.317C>G mutant human POC1B mRNAs. Yeast two-hybrid screening of a human retinal cDNA library revealed FAM161A as a binary interaction partner of POC1B. This was confirmed in coimmunoprecipitation and colocalization assays, which both showed loss of FAM161A interaction with p.Arg106Pro and p.G1n67del variant forms of POC1B. FAM161A was previously implicated in autosomal-recessive retinitis pigmentosa and shown to be located at the base of the photoreceptor connecting cilium, where it interacts with several other ciliopathy-associated proteins. Altogether, this study demonstrates that POC1B mutations result in a defect of the photoreceptor sensory cilium and thus affect cone and rod photoreceptors