Tail approximation for the chemical master equation

The chemical master equation is a differential equation describing the time evolution of the probability distribution over the possible “states” of a biochemical system. The solution of this equation is of interest within the systems biology field ever since the importance of the molec- ular noise has been acknowledged. Unfortunately, most of the systems do not have analytical solutions, and numerical solutions suffer from the course of dimensionality and therefore need to be approximated. Here, we introduce the concept of tail approximation, which retrieves an approximation of the probabilities in the tail of a distribution from the total probability of the tail and its conditional expectation. This approximation method can then be used to numerically compute the solution of the chemical master equation on a subset of the state space, thus fighting the explosion of the state space, for which this problem is renowned

k-Spectra of weakly-c-Balanced Words

A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by deleting some of its letters. That is, there exist the (potentially empty) words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and $w = v_0u_1v_1u_2v_2...u_nv_n$. We consider the set of length-$k$ scattered factors of a given word w, called here $k$-spectrum and denoted \ScatFact_k(w). We prove a series of properties of the sets \ScatFact_k(w) for binary strictly balanced and, respectively, $c$-balanced words $w$, i.e., words over a two-letter alphabet where the number of occurrences of each letter is the same, or, respectively, one letter has $c$-more occurrences than the other. In particular, we consider the question which cardinalities n= |\ScatFact_k(w)| are obtainable, for a positive integer $k$, when $w$ is either a strictly balanced binary word of length $2k$, or a $c$-balanced binary word of length $2k-c$. We also consider the problem of reconstructing words from their $k$-spectra

Urinary bladder melanosis with complete resolution case report

Background Melanosis of the bladder is a rare condition characterized by multifocal, diffuse melanin pigmentation of the urothelial mucosa or lamina propria without any proliferation of melanocytes. Less than 25 cases have been reported so far of which only four patients had concurrent urothelial carcinoma. Case presentation We are reporting a case of melanosis of the bladder in a 58-year-old female associated with pTaG1 transitional urothelial cell carcinoma (TCC) of the bladder who presented with symptoms of recurrent urinary tract infection (UTI). Cystoscopy and biopsy results confirmed benign melanosis. Conclusion Our case is unique because bladder melanosis associated low grade TCC with complete resolution of both conditions within one year

Approximation of event probabilities in noisy cellular processes

Molecular noise, which arises from the randomness of the discrete events in the cell, significantly influences fundamental biological processes. Discrete-state continuous-time stochastic models (CTMC) can be used to describe such effects, but the calculation of the probabilities of certain events is computationally expensive. We present a comparison of two analysis approaches for CTMC. On one hand, we estimate the probabilities of interest using repeated Gillespie simulation and determine the statistical accuracy that we obtain. On the other hand, we apply a numerical reachability analysis that approximates the probability distributions of the system at several time instances. We use examples of cellular processes to demonstrate the superiority of the reachability analysis if accurate results are required

Organized condensation of worm-like chains

We present results relevant to the equilibrium organization of DNA strands of arbitrary length interacting with a spherical organizing center, suggestive of DNA-histone complexation in nucleosomes. We obtain a rich phase diagram in which a wrapping state is transformed into a complex multi-leafed, rosette structure as the adhesion energy is reduced. The statistical mechanics of the "melting" of a rosette can be mapped into an exactly soluble one-dimensional many-body problem.Comment: 15 pages, 2 figures in a pdf fil

Vegetal diamine oxidase alleviates histamine-induced contraction of colonic muscles

Excess of histamine in gut lumen generates a pronounced gastrointestinal discomfort, which may include diarrhea and peristalsis dysfunctions. Deleterious effects of histamine can be alleviated with antihistamine drugs targeting histamine receptors. However, many antihistamine agents come with various undesirable side effects. Vegetal diamine oxidase (vDAO) might be a relevant alternative owing to its histaminase activity. Mammalian intestinal mucosa contains an endogenous DAO, yet possessing lower activity compared to that of vDAO preparation. Moreover, in several pathological conditions such as inflammatory bowel disease and irritable bowel syndrome, this endogenous DAO enzyme can be lost or inactivated. Here, we tested the therapeutic potential of vDAO by focusing on the well-known effect of histamine on gut motility. Using ex vivo and in vitro assays, we found that vDAO is more potent than commercial anti-histamine drugs at inhibiting histamine-induced contraction of murine distal colon muscles. We also identified pyridoxal 5′-phosphate (the biologically active form of vitamin B6) as an effective enhancer of vDAO antispasmodic activity. Furthermore, we discovered that rectally administered vDAO can be retained on gut mucosa and remain active. These observations make administration of vDAO in the gut lumen a valid alternative treatment for histamine-induced intestinal dysfunctions

On the Shuffle Automaton Size for Words

We investigate the state size of DFAs accepting the shuffle of two words. We provide words u and v, such that the minimal DFA for u shuffled with v requires an exponential number of states. We also show some conditions for the words u and v which ensure a quadratic upper bound on the state size of u shuffled with v. Moreover, switching only two letters within one of u or v is enough to trigger the change from quadratic to exponential

Unambiguous 1-Uniform Morphisms

A morphism h is unambiguous with respect to a word w if there is no other morphism g that maps w to the same image as h. In the present paper we study the question of whether, for any given word, there exists an unambiguous 1-uniform morphism, i.e., a morphism that maps every letter in the word to an image of length 1.Comment: In Proceedings WORDS 2011, arXiv:1108.341