Muller's ratchet with overlapping generations

Muller's ratchet is a paradigmatic model for the accumulation of deleterious mutations in a population of finite size. A click of the ratchet occurs when all individuals with the least number of deleterious mutations are lost irreversibly due to a stochastic fluctuation. In spite of the simplicity of the model, a quantitative understanding of the process remains an open challenge. In contrast to previous works, we here study a Moran model of the ratchet with overlapping generations. Employing an approximation which describes the fittest individuals as one class and the rest as a second class, we obtain closed analytical expressions of the ratchet rate in the rare clicking regime. As a click in this regime is caused by a rare large fluctuation from a metastable state, we do not resort to a diffusion approximation but apply an approximation scheme which is especially well suited to describe extinction events from metastable states. This method also allows for a derivation of expressions for the quasi-stationary distribution of the fittest class. Additionally, we confirm numerically that the formulation with overlapping generations leads to the same results as the diffusion approximation and the corresponding Wright-Fisher model with non-overlapping generations

Photodermatitis and ocular changes in nine horses after ingestion of wild parsnip (pastinaca sativa)

Background Primary photosensitization rarely occurs in horses and can easily be misinterpreted. Descriptions of the disease in horses after ingestion of parsnip are lacking. The aim of this case series was to describe the dermatological and ocular changes due to photosensitization and to raise awareness of parsnip being a possible aetiologic agent. Case presentation Nine horses from three different stables in Berlin and Brandenburg, Germany, presented variable degrees of erythema, scaling, crusting and necrosis of unpigmented skin at the head and prepuce. Horses were of different breeds with a median age of 15 ± 5.9 years. A mild leukocytosis was diagnosed in 1/9 horses at admission. Analyzed liver enzymes were within the reference ranges in all horses. Ocular changes were diagnosed as follows: blepharitis (3/9), conjunctivitis (7/9), corneal edema without additional signs of keratitis and/or uveitis (2/9), corneal edema with signs of uveitis (1/9) and photophobia (4/9). One horse developed a fluorescein positive corneal erosion. Skin biopsy (1/9) revealed a moderate to severe acute, eosinophilic and lymphocytic dermatitis with dermal edema and vasculitis. All stables housing these patients fed hay from the same distributer. Analyzed hay samples showed high contents of wild parsnip (plants, seeds, roots). Wild parsnip is widespread in Europe and contains furocoumarins, a family of photodynamic pigments, which may cause primary photodermatitis, keratoconjunctivitis and uveitis. Horses were treated according to severity of clinical symptoms systemically with flunixine meglumine (1.1 mg/kg BW 1-2x/day) or prednisolone (1 mg/kg BW 1x/day). Topically, either gentamicin (3x/day), dexamethasone (2-3x/day) and/or atropine (1x/day) were used. Skin care was provided with almond oil or dexpanthenol (2x/day). All horses were kept in a dark environment or were treated with sunscreen and facemasks. Duration of treatment varied from 6–30 days (median 11.3 days). Conclusion Ingestion of wild parsnip (Pastinaca sativa) can induce primary photosensitization with dermatitis and ocular injury in horses. In times of extreme weather, hay may alter in botanical composition, resulting in high amounts of uncharacteristic plants causing novel problems

Interacting Brownian Motion with Resetting

We study two Brownian particles in dimension $d=1$, diffusing under an interacting resetting mechanism to a fixed position. The particles are subject to a constant drift, which biases the Brownian particles toward each other. We derive the steady-state distributions and study the late time relaxation behavior to the stationary state.Comment: 13 pages, 4 figure

Phase transitions in large deviations of reset processes

We study the large deviations of additive quantities, such as energy or current, in stochastic processes with intermittent reset. Via a mapping from a discrete-time reset process to the Poland-Scheraga model for DNA denaturation, we derive conditions for observing first-order or continuous dynamical phase transitions in the fluctuations of such quantities and confirm these conditions on simple random walk examples. These results apply to reset Markov processes, but also show more generally that subleading terms in generating functions can lead to non-analyticities in large deviation functions of 'compound processes' or 'random evolutions' switching stochastically between two or more subprocesses.Comment: 8 pages, 6 figure

Feynman-Kac equation for anomalous processes with space-and time-dependent forces

Invited contribution to the J. Phys. A special issue Emerging Talent

A MITF Mutation Associated with a Dominant White Phenotype and Bilateral Deafness in German Fleckvieh Cattle

A dominantly inherited syndrome associated with hypopigmentation, heterochromia irides, colobomatous eyes and bilateral hearing loss has been ascertained in Fleckvieh cattle (German White Fleckvieh syndrome). This syndrome has been mapped to bovine chromosome (BTA) 22 using a genome-wide association study with the bovine high density single nucleotide polymorphism array. An R210I missense mutation has been identified within microphthalmia-associated transcription factor (MITF) as responsible for this syndrome. The mutation is located in the highly conserved basic region of the protein and causes a negative-dominant effect. SOX10 and PAX3 promoter binding site mutations in MITF could be ruled out as causative for the German White Fleckvieh syndrome. Molecular characterization of this newly detected bovine syndrome means a large animal model is now available for the Tietz syndrome in humans

Weakly non-ergodic Statistical Physics

We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum dots and the sub-diffusive continuous time random walk model. When the fluctuations become normal we recover usual ergodic statistical mechanics. Examples of a particle undergoing fractional dynamics in a binding force field are worked out in detail. We briefly discuss possible physical applications in single particle experiments

Run and tumble particle under resetting:a renewal approach

We consider a particle undergoing run and tumble dynamics, in which its velocity stochastically reverses, in one dimension. We study the addition of a Poissonian resetting process occurring with rate $r$. At a reset event the particle's position is returned to the resetting site $X_r$ and the particle's velocity is reversed with probability $\eta$. The case $\eta = 1/2$ corresponds to position resetting and velocity randomization whereas $\eta =0$ corresponds to position-only resetting. We show that, beginning from symmetric initial conditions, the stationary state does not depend on $\eta$ i.e. it is independent of the velocity resetting protocol. However, in the presence of an absorbing boundary at the origin, the survival probability and mean time to absorption do depend on the velocity resetting protocol. Using a renewal equation approach, we show that the the mean time to absorption is always less for velocity randomization than for position-only resetting.Comment: 16 pages, 1 figure, version accepted in Journal of Physics

A Glial Variant of the Vesicular Monoamine Transporter Is Required To Store Histamine in the Drosophila Visual System

Unlike other monoamine neurotransmitters, the mechanism by which the brain's histamine content is regulated remains unclear. In mammals, vesicular monoamine transporters (VMATs) are expressed exclusively in neurons and mediate the storage of histamine and other monoamines. We have studied the visual system of Drosophila melanogaster in which histamine is the primary neurotransmitter released from photoreceptor cells. We report here that a novel mRNA splice variant of Drosophila VMAT (DVMAT-B) is expressed not in neurons but rather in a small subset of glia in the lamina of the fly's optic lobe. Histamine contents are reduced by mutation of dVMAT, but can be partially restored by specifically expressing DVMAT-B in glia. Our results suggest a novel role for a monoamine transporter in glia that may be relevant to histamine homeostasis in other systems